A numerical method for solving of hypersonic nonequilibrium aerogasdynamics problems is suggested. The method is based on the full three-dimensional Navier-βStokes
equations, supplemented by the equations of chemical kinetics and the finite volume RKDG (Runge-Kutta Discontinuous Galerkin) method. The developed algorithms are implemented in the computer-aided software package SIGMA. The results of simulation of a hypersonic flow about a spherical nose segment of a model hypersonic vehicle are presented.