In this paper a mathematical model and a computational technique for the static analysis of multi-support stepped spindle shafts on nonlinear elastic supports are presented. On the basis of the Timoshenko differential equation of the beam's bent axis and the method of initial parameters, a resolving system of equations is obtained that takes into account the nonlinear dependency of the stiffness of the bearings on the forces acting on them along with the stepwise variation of the cross-sectional dimensions of the shaft. A numerical method for solving the problem has been proposed and a software tool has been developed, which performs the static analysis of multi-support stepped spindle shafts on nonlinear elastic supports in MATLAB environment.