feels like rear end is loose

Whe I give the truck gas the rear axle feel like it is moving. I rebuilt the hog head and no improvment. It only does this sometimes. I have checked the leaf spring bolts and everything else I can think of. I don't know what else to do. HELP?

I had a Ranchero that did that. Everything seemed tight. (U bolts, shackles, front spring mount. etc.) Found that the center bolt that runs through the leaf springs was sheared off on one side. The rear axel was not moving far, but the shift of position of the rear end could be felt when accelerating hard.