In this paper, we consider “sinus-lifting motion” which is the effective motion of a snake for rapid movement consisting of lifting some parts of its body off the ground, and switching the lifted and grounded parts dynamically. This motion is analyzed based on control theory. We focus on the constraint force of passive wheels and switching of grounded parts of the snake robot to minimize the constraint force. Simulations show that the motion that minimizes the constraint force of the snake robot is similar to the sinus-lifting motion in appropriate amplitudes and periods of the body shape.