There are a couple of reasons your Truck Would Shake While Accelerating. One reason could be a Bad U-Joint. Failed U-Joints will cause the Driveshaft to be out of alignment. When it is out of alignment it will cause a Vibration. One obvious sign of Bad U-Joint is rust around the caps. Another sign could be cracked or broken caps. Either way, if your Driveline has play or movement. Then you need to get the U-Joints replaced as soon as possible.