Re: No pain, but tendon \"pops\" back and forth under elbow.
I think I know what you are describing because I have had something similar. What you are feeling is your ulnar nerve (it's the "funny bone") sliding back and forth across your elbow. This is causing that "popping" sensation.
What's interesting is that you say you are not feeling pain. I can tell you from experience that if you continue to irritate the nerve by doing exercises that cause it to "pop", it will start to hurt and you will feel other symptoms like coldness and tingling in your ring and pinky fingers. Basically, this is the nerve flaring up.
I was diagnosed by a doctor specializing in arm/hand issues and the upshot is that you have to modify your exercises so that you irritate the nerve as little as possible. So, for me that means a somewhat wider grip on bb bench presses, stopping at roughly 90 degrees on bicep curls, and avoiding altogether skullcrushers.