Viscous simulations of shock-bubble interaction and Richtmyer-Meshkov instability are performed using an explicit high-order computational method. The simulations are performed by solving the Navier-Stokes equations associated with two convection equations governing the interface between two fluids. The stiffened equation of state is used to relate the pressure to the total energy of a liquid or a gas. Two-dimensional two-phase flows are considered. The first flow concerns the Richtmyer-Meshkov instability developed on a post-shocked interface between air and sulphur hexafluoride (SF6). The influence of the grid refinement on the instability shape is studied. The second problem deals with a shock wave propagating in air and hitting a cylindrical bubble filled with helium or chlorodifluoromethane (R22). A spatial-time diagram represents the locations of the various pressure waves generated from the interaction between the shock wave and the interface. For both simulations, the numerical results are in agreement with experimental data and visualizations.