In this paper the applicability of a statistical linearization procedure is evaluated as a practical design tool to predict the lateral stability and forced response of a locomotive with axle clearance, hardening longitudinal primary stiffnesses, wheel/rail profile, and centerplate friction nonlinearities. A digital lateral model with random inputs is compared to the results obtained by the statistical linearization method. Gaussian and trapezoidal density functions are used and it is shown that the assumption of a trapezoidal density function reduces the difference in r.m.s. values to less than 15% for both low and high speed cases where the assumption of a Gaussian density function yields differences as great as 31%. This method predicts the frequency content of the signals as well as the r.m.s. values.