Use a hi-lift. Jack up the truck and fill in below to break the suction before applying lateral force. Use of a kinetic strap is then recomended, as they used, minus the projectiles. Two straps can be joined with a rolled up magazine or small stick to keep them from making a knot. Give it a good yank or two, and see if it works.

If that does not work... break out the winch and the snatch block. A winch pulling at double capacity (ie, with a snatch block), should yeild enough force to remove the truck, but may take multiple iterations of rigging. The winch is always the safer extraction method for the vehicle, but caution should be exercised due to the possability that the winch cable can snap and be a danger to bystanders.

I have been stuck in that kind of mud and needed to be winched out. Using a shovel would be really hard work as that mud is really heavy, but that might be required as prep for the high lift to find some more solid ground below. Plus some type of plywood board for the jack to stand up on so that the pressure on the soft bottom will be spread.

Also they use those plastic traction aids....but they don't shovel near the tires they just stick them in the mud. Like they are magically going to find their way under the tires.

Maybe some digging around the vehicle, all the mud around the wheels and diffs are creating a lot of resistance. Plus you can see if you are caught on something. In one shot I see some tire in the mud, front right tire. It's like a motocross tire. Maybe the rest of the bike down in there....who knows.......

When I was stuck in mud like that I was lucky that the other truck that winched me out had a powerfull enough winch to just pull me out without digging and the stuck truck was a F150.

Nice guys, great responses!

I think all of the possibilities have been said. A jack might work well, but I don't think shoveling would ever work. My friend who is in the army said short of the tank of course, they pull really stuck vehicles out with some really thick rope and a bunch of turn around blocks. He said they used 16:1 ratios on the really heavy, really stuck vehicles. I bet without carrying too much rope, with a 4:1 ratio the near death experience would have been avoided. IMO, leaving the truck in the mud was a better option than doing what they did.

Oh Yeah aeathb, Shoveling around the truck would have been really hard, and the mushy mud would likely just fill back into whatever hole you just created. But if you have no other choice, you will just have to do it. And even after you have shoveled you will still likely need to be pulled out because you'll probably spin the tires into the soft ground. But....This for sure will make you learn in a hurry, to never cross mud without knowing what you are getting into and if there is no one to pull you out. Guys who do lots of mudding I have noticed often have a designated truck, which stays way out of the mud, with lots of cable length on a good strong winch and whenever they get stuck, they hook up the winch and get pulled out, no shoveling, no traction aids, no problem. Crossing this kind of mud, you will get stuck, just a question when and how stuck.