The paper considers the probability of applying the generalized polynomial chaos for studying the stability of stochastic dynamical control systems with probabilistic uncertainty. Types of uncertainties are determined. They are presented and evaluated. The ways of their accounting for while studying the stochastic dynamical control systems are explained. Many orthogonal polynomials are described, their properties are analyzed. The transformations in the form of orthogonal polynomials are obtained for different probability-density functions of uncertainty. The author gives an example of practical application of the generalized polynomial chaos for simulating the stochastic system, which allows presenting the original system in the form of the determinate one, but with higher dimensions. As a possible way of studying the stochastic systems with uncertainty, the Cauchy probability density function is also considered.