Features of computing shock waves in variables density, velocity and pressure by a numerical technique developed by the authors based on the method CIP-CUP have been investigated. One of important merits of the method is that it allows one to evaluate, without explicit separation, shock waves and contact discontinuities of gas-liquid type. It has been shown that computation of shock waves in liquid with essential entropy jump leads to unphysical oscillations in the vicinity of their fronts and gives significant errors in characteristics of the flow behind the shock front and velocity of its propagation Introduction of artificial viscosity allows one to remove all these problems. Introducing artificial viscosity in the equations for velocity and pressure gives numerical solution with total energy conservation (apart from conserving mass and momentum) on the shock front, while introducing it in the velocity equation only leads to solution with entropy conservation.