The interaction of shock fronts with molecular clouds is investigated. For this purpose, a two-fluid model describing an H-H2 gas mixture is applied. The resulting equations are solved with a 2D axial-symmetric, fully compressive hydrodynamics code. Radiative cooling and the thermodynamical properties of the H2 molecule, ie. rotational and vibrational degrees of freedom as well as thermal dissociation, are taken into account. The evolution of the shock/cloud system using this more sophisticated thermodynamical model is found to be very different from that involving a pure atomic H gas which obeys the ideal gas law. For example, the maximum density of the shocked cloud is about 5-10 times lower in the latter case. This significant result might become very important when estimating triggered star formation rates. Another difference is that in the case of H-H2 mixture, the shocked cloud gets a comet-like structure because of a smaller reexpansion. From the numerical experiments we conclude that the application of the ideal gas law is insufficient and gives only a crude approximation of the real dynamics of a shock/cloud collision.