Q: Are there any exercises that will help strengthen the upper chest muscle without using gym equipment?

A: Incline bench press is definitely the single best upper chest exercise. However if you don't have access to the gym, you can still do push-ups, which are one of the most popular and simple exercises. Lie on floor on your stomach, with hands a bit wider than shoulder width. Raise your body up off the floor by extending arms keeping the body straight, so your knees are off the floor too. Then reverse the movement and lower your body back to the floor. Repeat. To make the exercise harder and to target the upper chest more, elevate your feet off the floor. Put them on a sofa or a chair, but keep your hands on the floor. Your body will be at an angle to the floor now, but still straight while you perform the exercise. The higher your feet are, the more difficult this exercise becomes and the more it will target upper chest and shoulders. You can even ask a partner to place a weight on your upper back to add more resistance while performing this exercise. If you can achieve the combination of feet elevation and/or extra weight that causes muscular failure in under 12 reps of this exercise, then you will have come very close to dulicating the effects of doing incline bench press in the gym. Keep in mind however that if you use too steep an angle for elevated pushups, you'd shift almost all the work to your shoulders and away from upper chest, so keep your angle of incline to no more than 30-45 degrees.

If you do not have enough strength to keep your legs straight while performing this exercise, keep your knees as well as your feet on the floor and only elevate your upper body. After awhile you'll build up enough strength to do regular push-ups.

Another point to consider is that shoulder strength, specifically anterior deltoid (front shoulder) is very complementary to upper chest strength since most movements that involve one of those muscles will also involve the other. Therefore you can also work on your shoulders with shoulder presses that you can do at home with a gallon of milk in each hand, for example. Though you are likely to outgrow such small resistance quickly and may want to buy some heavier dumbbells for home if gym is not an option.