In this paper we present the mathematical modelling in a hydraulic ram pump (HRP) system and an explanation of the simplified working cycle of its action. The flow in the HRP system is unsteady; therefore, unsteady pipe flow equations and the method of characteristics (MOC) are given. The mathematical modelling of particular components of the HRP system is explained in detail. The drive and delivery pipes are modelled by e fixed grid MOC, and the suply and delivery tanks are the boundary conditions - open reservoirs with a constant water level. The HRP is modelled as a unit boundary condition describing the physics of its action. This boundary condition consist of 11 equations with 11 dependent variables and is solved by an iterative procedure for each time step of the computational run. The derived model is programmed for a digital computer. A computer simulation using input data from the literature is made and the results are presented in the form of pressure and velocity vs. time graphs.