Snake-inspired robots display promise in areas such as search, rescue and reconnaissance due to their ability to locomote through tight spaces. However, several specific issues regarding the design and analysis must be addressed in order to better design them. This thesis develops kinematic and dynamic models for a class of snake-inspired gait known as a rectilinear gait, where mechanism topology changes over the course of the gait. A model using an Eulerian framework and Coulomb friction yields torque expressions for the joints of the robot. B-spline curves are then used to generate a parametric optimization formulation for joint trajectory generation. Exact gradient computation of the torque functions is presented. A parametric model is used to describe the performance effects of changing system parameters such as mass, length, and motor speed. Finally, a snake-inspired robot is designed and fabricated in order to demonstrate both the vertical rectilinear gait and a modular, molded design aimed at reducing the cost of fabrication.