How can I get my arms strong enough to do a push up?

I've been working out for a little over a week now, and I am trying so hard to improve in several areas, but I'm not seeing results when I attempt a pushup daily. I hold myself up for 60 seconds trying to go down as far as I can and then coming back up, but I'm not feeling the "after burn" that I would think I would have to tear muscles and build them back up. What types of exercises should I be doing and for how long so that I begin doing pushups?

Certainly, if you cannot do a push-up now, I would work (or train) to be able to do them. Starting with a simple bench press in an adaptation phase. Start with the Olympic bar only and do two sets of twenty reps (2 x 20). Twice a week is enough, and slowly add weight. In the adaptation phase of doing 2 x 20's, you don't want much weight at all. After your body has adapted, then add some small plates, lower the number to 2 x 10. Try and keep your hands at the same width you would use for a push-up. You could also do the same with the lat pull down machine at the gym and the tricep press using an adaptation phase of two or three weeks before increasing the weight.

This will slowly build up your ability to complete a push-up and then successive push-ups. If you don't have access to weights or a gym, you could adapt with doing push-ups with your knees on the floor and work your way up.

Be patient - Rome wasn't built in a day (or a week!)

Bump - for all the great advice!

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