How to Perform the Barbell Close Grip Bench Press
The triceps brachii is comprised of three muscle heads - the long, lateral, and medial heads. When these three heads are evenly developed they create the appearance of a horseshoe or upside-down U when flexed.
Bodybuilders looking to naturally increase their arm size as rapidly as possible should focus on compound and isolation movements targeting the triceps, rather than the biceps. Powerlifters who grind through the midpoint of or fail to lockout their bench press reps should hammer their triceps with compound movements.
The triceps are primarily built through pushing movements such as presses and extensions. These movements may be performed in a vertical or horizontal plane. Every balanced physique needs a beastly set of triceps.
The barbell close grip bench press is a compound push exercise targeting the triceps brachii, comprised of the long, lateral, and medial heads. The anterior or front deltoid as well as the sternal and clavicular heads of the pectoralis major act as supporting muscle groups during this movement. 
Supporting muscle groups assist the target muscle group in completing the movement. The biceps brachii (short & long heads) acts as a stabilizer during this exercise.  Stabilizer muscles help maintain a posture or fixate a joint by contracting without significantly moving. 
The close grip bench press is consistently ranked one of, if not the best compound movement for adding tricep size and strength.
How to Perform the Barbell Close Grip Bench PressApproach the flat barbell bench apparatus and select the appropriate working weight. Ensure you add an even amount of weight to both sides of the bar. don't place 75lbs on one sides and 100lbs on the other side.
Uneven loading won't improve your gains and will likely lead to an injury. If this is your first time performing the exercise then pick a conservative weight that you can safely lift for 8 to 12 repetitions. Most trainees find that when the number of reps is held consistent, they'll use less weight on the close grip bench press compared to the flat bench press.
Once you've selected the appropriate working weight place your feet flat on the floor and lay backwards so that you're face-up with your head, upper back, and glutes completely touching the padded support. Keeping your chest high, shoulders down, and squeezing your shoulder blades and upper back together, grasp the bar with a shoulder-width traditional pronated grip (thumbs wrapped around the knuckles and palms facing away from you).
An excessively narrow grip decreases range of motion, internally rotates the shoulders, and places unnecessary stress on the wrists. An excessively wide grip move emphasis from the triceps to the chest muscle fibers.
After setting your grip take a deep breath, brace your abdominals for impact, and with the assistance of a spotter or by yourself lift the barbell off the pins. Position the barbell so that it's vertically in-line with your arms and shoulders.
Lower the barbell towards your chest in a controlled motion. As you lower the barbell ensure your elbows stay close to your torso, chest stays up, shoulders stay retracted, and upper back remains squeezed. Once the barbell hits the required depth, which for most will be touching or slightly above the lower portion of the pecs, hold for 0 to 5 seconds. After holding in the bottom position for the desired duration press the bar upwards until the arms and elbows are straight (but not hyperextended).
The movement pattern for both the lowering and pressing of the bar should be the same. If you find your elbows flaring and moving away from your torso then the weight is too heavy. Some lifters choose to exhale while pressing the barbell or in between in each repetition. Choose a breathing pattern that feels the most natural and comfortable for you.
This exercise can be performed using straight sets, pre-exhaust sets, drop sets, rest-pause sets, supersets, trisets, giant sets, paused reps, partial reps, forced reps, or slow negatives. As with any exercise, the two most important components are high-quality form and progression. Progression can take a variety of forms (e.g. more weight, sets, or reps, decreased rest period, improved rep quality, etc...) but strive to improve every training session.
Close Grip Bench Press Form TipsHold at the Bottom - If you're looking to increase intensity then experiment with holding the barbell at the bottom position, touching or slightly above your chest, for 5 to 10 seconds. don't relax your muscles and simply let the barbell rest on your body; this is a recipe for serious injury.
This hold will not only stretch your triceps but will also increase time under tension. Increased time under tension is an excellent variable to adjust for progressive overload and enhanced muscle growth.
Stay Tight - Staying tight throughout the entire movement minimizes the likelihood of injury. If you've ever seen someone lose tightness during the lowering or pressing portion of the bench press, then you know just how severe the consequences can be. Staying tight begins with a proper setup prior to removing the bar from the pins. Keep your elbows close to your torso, chest up, shoulders down, and squeeze your shoulder blades together as hard as possible.
Those cues, combined with taking a deep breath and bracing your abdominals for impact prior to unracking the bar, will ensure your triceps, shoulders, and pecs stay healthy for a longer period of time.
Avoid Momentum - The barbell close grip bench bench press provides maximum benefits when it's perform in a controlled full-range of motion. Check your ego at the door and don't immediately attempt 225lbs if your 1-rep maximum on the flat barbell bench press is only 135lbs.
In addition to staying tight and keeping your head, glutes, and upper back on the padded support, do not bounce the bar off of your chest. This momentum dramatically increases the likelihood of injury and minimizes the stimulus of the target muscles.
Avoid the False Grip - Do not use the false grip (thumbs and fingers wrapped around the same side of the bar) unless you have a preexisting injury preventing you from using the traditional grip (thumbs wrapped over the knuckles). While many trainees find they're able to press slightly more weight using the false grip, the likelihood of the bar rolling out of your palms and on to your chest or neck exponentially increases.
If you insist on using this unsecure grip ensure you have a spotter or safety pins in place in case you lose control of the bar.
Five Points of Contact - Throughout the entire lift your feet should be flat on the floor and your head, glutes, and upper back should be touching the padded support. Keeping all five points of contact will help ensure you stay tight and encourage the completion of high quality repetitions.
References1) "Barbell Close Grip Bench Press." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 3 Nov. 2015.
2) "Kinesiology Glossary." ExRx (Exercise Prescription) on the Internet. N.p., n.d. Web. 3 Nov. 2015.