Abstract The forced oscillations of a four-axle vehicle with a double spring suspension are considered. The motion of a system with six degrees of freedom can be represented with sufficient accuracy by a system with two degrees of freedom. Therefore, the body of the vehicle has two degrees of freedom: sideways movement and wagging (jumping and galloping carts will be neglected). It is assumed that the rheological properties of the spring (suspension) are different and obey the hereditary theory of Boltzmann-Volterra viscoelasticity. As the core of heredity, the Koltunov-Rzhanitsyn core is used, which has weakly singular features of the Abel type. Effective computational algorithms for solving problems based on the use of quadrature formulas have been developed. For numerical calculation, a computer program has been compiled, the results of which are presented in the form of graphs. The influence of the rheological properties of the suspension on the forms of vertical and angular movement of the body is studied. It was found that due to the suspension viscosity, the amplitude of vertical and angular oscillations decreases and the frequency increases.