2001 Jeep Cherokee Rear End

My Jeep when comes to a complete stop, there is a (thud) which you can feel as well as hear in the rear end. It also occurs when accelerating from complete stop. It doesn't happen every time, but enough to know that there is something wrong. I have taken my Jeep to an close friend whom is an mechanic. He check U-joints and for anything that might be loose and found nothing. He opened rear differential gear cover too. I also took it too a Transmissions / Differential specialist and he too could figure it out. This baffles me because this (thud) is an obvious problem and no one can help me. I'd like to fix the problem because I would like to keep my Jeep Cherokee Sport for several more years. It happens when I brake and accelerate only.