Numerical modeling of heterogeneous (multiphase) mixtures or, in particular, gas suspensions (mixtures of gases with solid particles) is one of the important directions in the study of the dynamics of complex hydrodynamic systems. The study of mathematical models of multiphase system is relevant, primarily from the point of view of applications. Such flows are often encountered in problems of aerodynamics, chemical technology, combustion physics, and others. The study of the influence of suspended particles on the hydrodynamic stability of two-phase flows requires, firstly, a thorough analysis of mathematical models of two-phase media and, secondly, the development of an effective, reliable mathematical apparatus for numerical simulation of hydrodynamic stability equations. In this article, for numerical modeling of the equations of stability of two-phase flows, it is proposed to apply the method of preliminary integration, where Chebyshev polynomials of the first kind is used as basis functions. The essence of the method lies in the fact that before solving the problem, the series in Chebyshev polynomial is pre-integrated the required number of times. Then the integrated series are used in a differential problems and a generalized algebraic eigenvalue problem with complex matrices and vectors is obtained, which is solved by standard methods.