shaking in 4-low

The past few times i have towed someone stuck on the beach (with a 96 xj sport) it has done some rough shaking after being in gear for a while. It doesn't happen immediately but after i have dragged them a ways i get this violent shaking. After i let off of the gas and come to a stop, it will happen again once i've advanced them some more. I'm sure they're differentials must have been dragging in the sand with a lack of ground clearance-but i'm just wondering if the shaking is a result of gradually towing someone in the sand or if there could be something wrong somewhere in the drivetrain. Also, both times afterwards it made several highway trips with no trouble. Any help or suggestions would be greatly appreciated.

It could be axle wrap / spring wrap / wheel hop. I've experienced it on sand before. Not sure how to avoid it other than an anti-wrap bar. You might try playing with tire pressure, or just let off the gas when it happens. Powering through it is the worst thing you can do, it'll lead to u-joint failure and will kill your leaf springs. Another thing you can try is driving on firmer sand closer to the water line.