ABSTRACT We present a new analytic fitting profile to model the ram pressure (RP) exerted over satellite galaxies on different environments and epochs. The profile is built using the information of the gas particle distribution in hydrodynamical simulations of groups and clusters of galaxies to measure the RP directly. We show that predictions obtained by a previously introduced β-profile model cannot consistently reproduce the dependence of the RP on halocentric distance and redshift for a given halo mass. It features a systematic underestimation of the predicted RP at high redshifts (z > 1.5), which increases towards the central regions of the haloes and it is independent of halo mass, reaching differences larger than two decades for satellites at r < 0.4Rvir. This behaviour reverses as redshift decreases, featuring an increasing overestimation with halocentric distance at z = 0. As an alternative, we introduce a new universal analytic model for the profiles that can recover the RP dependence on halo mass, halocentric distance, and redshift. We analyse the impact of our new profile on galaxy properties by applying a semi-analytic model of galaxy formation and evolution on top of the simulations. We show that galaxies experiencing large amounts of cumulative RP stripping typically have low stellar masses (M⋆ ≤ 109.5 M⊙). Besides, their specific star formation histories depend on the RP modelling applied, particularly at high redshifts (z > 1.5).