How are you trying to improve your push ups?
Are you just trying to do more and more push ups?
Push ups are not as easy as they seem, and there is more technique involved than most realize. Being a bodyweight movement most people do these for a high volume so it is beneficial to make sure you have a good shoulder position throughout the entire range of motion so that you do not create overuse issues. Not everyone has the mobility (range of motion under tension) to perform a push up all the way to the floor so make sure you are strengthening what range you have before forcing yourself into a full depth push up. The shoulder blades should stay down during the entire range of motion and not slide up at the bottom like they will try to do. If the deltoid (shoulder) moves closer to the ground then the pecs at the end range then you do not have the mobility for that range yet.
If this looks familiar I would recommend scaling your push ups until you can maintain the correct position through the full range of motion.
Elevated Push Ups: This will allow you to maintain good tension and correct shoulder position throughout the entire range of motion. By elevating the upper body we can take weight away from the movement. Since this is a bodyweight movement then there is only one weight so we must find ways to reduce the amount that we are pressing until we can maintain the correct tension and a good position for the full range of motion.
In the meantime I would add in accessory work that will help you strengthen the muscles that will be involved in maintaining tension throughout the range of motion.
Here are some recommendations:
Dumbbell Bench Press: This will allow you to move weight at a full range of motion. The dumbbells will allow for you to train stability in the shoulder as well as strengthening the pecs and triceps. Coaches note: make sure you are bringing the shoulder blades down and together before laying on the bench so that it will keep the shoulders in a good position through the full range of motion.
Plank Holds: This will strengthen the position you must hold in order to perform a push up. Just like what you are trying to accomplish with the push up make sure you are keeping the shoulders in a good position. An RKC plank will benefit even more because you must create max tension for a shorter period of time. Coaches note: pull the shoulders into a good position and instead of planking for a long time squeeze every muscle as hard as you can from head to toe for 10-15 seconds and do that for reps.
Chest (Pec) flys: These will help you learn to control the pecs at an extended range of motion. When we are weak in the bottom of the push up it is usually because the pecs do not work as efficiently at the longer length and the shoulders and traps try to take over. The pec fly will allow the pecs to become stronger at the end ranges of motion. Coaches note: focus on maintaining tension in the pec the entire range of motion and only going as far as possible through your range of motion under tension and not allowing pointless reps.
Tricep extensions: The triceps should be the secondary muscles involved in the push up so we should add movements to strengthen these as well. These can be done from many different angles depending on your skill level but if we are looking to improve the push up specifically then I would recommend doing them in a similar position. Lying on your back with the arms straight overhead and only bending at the elbows while the shoulders maintain a down and back position. These can also be done face down with some rings or a bar to add in the core stability of a plank. Coaches note: we are working the triceps so make sure you are not cheating with whatever level you try and choose a weight that you can move correctly.
Try adding these accessory movements into your push up program. I would recommend starting at 3-4 sets of 10-12 reps of the exercises and 3 sets of 10-15 seconds on the RKC plank. This could be done 2 times a week on an upper body focused day to help improve your push ups.