The monograph summarizes the results of research of many years in the field of numerical simulation based on the continuum dynamics equations for transonic and supersonic flows of viscous perfect gas in the context of the problems of external aerodynamics, which have been obtained by the authors and their colleagues and published in different domestic journals. The monograph consists of two parts. The first part deals with stationary and non-stationary two-dimensional problems, stationary three-dimensional problems are considered in the second part. That said, the uniform steady flow over the bodies of comparably simple configuration, which surface is determined analytically, is studied. Each part begins with mathematical statement of the problem and method of its numerical analysis. This is followed by the detailed discussion of the results of computations for a number of aerodynamic problems, which have been obtained within some range of the key similarity parameters. The problems under consideration are divided into two groups according to the purposes. The problems intended to the theoretical study of the flow field near the streamlined body, its local and total aerodynamic characteristics and of the effect of the key similarity parameters on the flow field characteristics refer to the first group. For this purpose it is necessary to obtain computational results within a wide range of the key similarity parameters. Such research is usually performed using the bodies of simple configuration, with the great attention being paid to the verification of the numerical simulation method and adequacy of the results. The monograph considers the classic bodies such as: circular and elliptical cylinders, sharp circular and elliptical cones. The problems related to the computational validation of the aerodynamic experiment in different supersonic and hypersonic wind tunnels of TsAGI refer to the second group. In this case the computations are implemented for the considered body as applied to the experimental conditions. That said, in most cases the computations include estimation of the flow field along the whole channel of the wind tunnel, i.e. the flow of the actuating medium is calculated in the nozzle and in the test chamber of the wind tunnel both with and without the model in it. The results of computations are compared with the experimental data. The monograph considers mainly the axisymmetric blunted bodies of Martian probe type (United States and European analogs). The monograph is of interest for professionals in the field of computational and applied aerodynamics as well as for undergraduate and graduate students whose major is somehow related to the applied aerodynamics.