Is push up a good excercise?

I like pushups or plank for abdominal strength. It can be hard on the shoulders and neck if you are starting off with weakness and soreness there. I recommend beginning with other exercises (free weights or upper body machines in the gym) before trying to work with your own entire weight. That said, you might want to try some out and see if you tolerate them. Pushups are good when you are ready fro them. You might also begin with baby pushups (knees on the floor).