This paper describes the mathematical model of the suspension of a robot traction of crawler type, in order to reduce mechanical vibrations caused by operation of the motors and overcoming obstacles in a path. The analysis in reference becomes relevant to the extent that the mechanical vibrations generated damage to the structure and electronic elements in this when the natural frequency of them is reached. The mathematical model of the suspension is based on the Newton-Euler method, which allows to obtain the differential equations conformed by forces and torques acting on the robot in motion. The robot in question, has an additional degree of freedom because the caterpillars are not fixed to 90 degrees, but can have a different angle of opening. As a result of analysis and mathematical model, the constants of elasticity and damping are adjusted so that the system acquires a response, such that the sprung mass has a minor impact on the vibrations generated in the distance covered.