This paper is focused on the solution of simple beam continually supported by elastic (Winkler's) foundation. The foundation contains longitudinal nonlinearity. For the calculation of displacements and bending stresses are used analytical procedures (approximate solution in the form of polynomial function) and probabilistic approaches (SBRA method, Monte Carlo Simulation Method, AntHill software). Probabilistic approach includes influences of variability of load, shape and material of the beam, and variability of modulus of the foundation. Probabilistic approach is used for the reliability expertise of the beam and calculation of safety
