In this paper a transport equation (TE) is derived that matches closely (within the limitation of an infinite target) the transport model in the Monte Carlo code TRIM. Initially, the authors derive a TE that incorporates an arbitrary free-flight path length distribution function and a stopping energy. From this TE a coupled set of integral equations (for spatial moments up to order four) incorporating the liquid free-flight path model used in TRIM is derived. Also, for the gas-like model of the free-flight path length distribution, the equivalence is shown between the new TE and the LSS backward linearized Boltzmann equation extended by Brice to include an intermediate energy.