I have a 1998 Chevy Suburban...What causes the truck to shake at the minimum...

[Takanori]

...speeds between 35 and 50 mph.? I have checked my tires and alignment. I get the shakes only at these speeds.

[jpcook]

check your front bearings and suspension

[Jordan]

You probably need to replace the spark plugs in your engine area.
I had this problem once before with my old car and once I got the spark plugs changed, the shaking stopped.
The plugs cost about 20-30 dollars at most.

The reason it's shaking is because the cylinders are missing causing it to run on fewer cylinders than it should be running on.

Good luck!!!