Popping/flexing, but *not* when pedaling hard My road bike is making very noisy popping/flexing sounds when pedaling. There are multiple sounds in a semi-regular pattern with each pedal stroke, and I can feel extra movement through the pedals as I hear the sounds. 

The sounds are most pronounced at moderate intensity and still present at light intensity, but when I do a hard sprint or threshold effort (i.e. when the drive-train is under constant pressure) the sounds disappear. 

Also, if I grab a pedal with my hand and press my weight down on the crank, I can feel some give and hear a sound as I do this.
I would suspect a problem in the bottom bracket, but would also check pedal spindles and bearings.

Check for any movement or play between:
- The pedals and crank arms
- Crank arms and crank axle
- Crank axle and the bottom bracket shell

If there is movement between the crank arms and crank axle don't ride the bike. Alloy cranks moving on steel axles will be irreparably destroyed.  

Check that the pedals turn smoothly, and the crank turns smoothly in the bottom bracket. It helps a great deal if you get the chain off the rings when you make the latter check. 

If there is play, 'hitches', 'notchiness' or a grinding feeling when turning the pedal or crank, the bearings are wearing out / worn out.

You have not said what material frame you have or what bottom bracket type you have but some press fit bearings tend to be creaky.