The present chapter gives a brief account on the methods of determination of probabilistic characteristics of motion of mechanical systems subject to random forces. In the introductory sections we give the required definitions of random variables and processes. In the definition of the probabilistic characteristics, we shall be mostly concerned with the correlation level when the expectations and correlation function are determined under the condition that these characteristics are given for the exterior forces. For the stationary processes, the Fourier transform is used and the spectral densities are defined. For statistically linear systems it proves possible to find an exact solution. However, nonlinear systems can be treated only by approximate methods (the methods of statistical linearization and statistical modeling). The method of the solution of the Fokker-Planck-Kolmogorov equation, mentioned at the end of this chapter.