My 95 F-350 does the same thing.I havent looked into it yet but Ive heard that the transfer-case mount is a common cause.The slip-yoke needing grease is another common one-as someone already mentioned.

 

This may sound stupid, but I had a thump rattle sound a while back on take off. After checking almost everything, changing mounts and bushings, it turned out to be oil bottles and a can of WD40 in a draw under the passenger seat. I laughed pretty hard when I figured it out

 

Well, I know this is not F0rd related, but my firebird did it and it was the tranny mount it would make like a hard thump you could feel in the floor board.. The tranny moutn was shot. My trucks starting to do it to..lol Like everybody els I might check the tranny mount. My 2 cents.

Adam Throop

 

I concur with Blue89F150. Sounds like a tranny mount. You have to push up hard on them sometimes to check. It might feel ok, but there is a lot of upwards pressure on them when step on the gas.... Put a long screw driver or lug nut wrench between the tranny and the crossmember if you can. Look at the rubber and see if it separates.