Numerical simulation of a super-and hypersonic flow of an inviscid gas around a sharp cone is performed taking into account high-temperature effects. The numerical implementation of a computational procedure designed to find stationary solutions of the gas dynamics equations describing flows around a cone with the real gas properties is carried out. The influence of physical and chemical processes on the distributions of flow quantities and the angle of inclination of the shock is discussed, and the results of numerical calculations obtained with the perfect and real gas model are compared. The computational results are compared with the data obtained for a supersonic around a wedge with a similar opening half angle.