We develop a new numerical approach to describe the action of ram pressure stripping (RPS) within a semi-analytic model of galaxy formation and evolution which works in combination with non-radiative hydrodynamical simulations of galaxy clusters. The new feature in our method is the use of the gas particles to obtain the kinematical and thermodynamical properties of the intragroup and intracluster medium (ICM). This allows a self-consistent estimation of the RPS experienced by satellite galaxies. We find that the ram pressure in the central regions of clusters increases approximately one order of magnitude between z = 1 and 0, consistent with the increase in the density of the ICM. The mean ram pressure experienced by galaxies within the virial radius increases with decreasing redshift. In clusters with virial masses M(vir) similar or equal to 10(15) h(-1)M(circle dot), over 50 per cent of satellite galaxies have experienced ram pressures similar to 10(-11) h(-2)dyn cm(-2) or higher for z less than or similar to 0.5. In smaller clusters (M(vir) similar or equal to 10(14) h(-1)M(circle dot)) the mean ram pressures are approximately one order of magnitude lower at all redshifts. RPS has a strong effect on the cold gas content of galaxies for all cluster masses. At z = 0, over 70 per cent of satellite galaxies within the virial radius are completely depleted of cold gas. For the more massive clusters the fraction of depleted galaxies is already established at z similar or equal to 1, whereas for the smaller clusters this fraction increases appreciably between z = 1 and 0. This indicates that the rate at which the cold gas is stripped depends on the virial mass of the host cluster. Compared to our new approach, the use of an analytic profile to describe the ICM results in an overestimation of the ram pressure larger than 50 per cent for z > 0.5.