This study introduces a generalized model for the shape of the sea floor which is relevant for ships during grounding. The sea floor is characterized as a paraboloid that allows a parametric modeling of the sea floor topology. Nonlinear explicit Finite Element (FE) code LS-DYNA was used to simulate the ship grounding scenarios. The simplified formulae to estimate the average grounding forces are proposed. The analytical formulae show reasonable agreement with the results from FE simulations. A simple computer program was used to simulate the ship response, which is assumed to be two- dimensional rigid motion, i.e. surge, heave and pitch. The results show that the sea floor topology is indeed a key parameter in the response analysis of a ship bottom during grounding. The penetration induced by the ship motion is also a function of ship motion. The envelopes of shear force and bending moment which are induced during grounding are checked against the DNV's still water requirements. The ultimate goal of the analysis is to allow prediction of the risk of penetration into cargo tanks with oil spill as a result, the risk of hull girder failure and estimation of the required tug force for pulling the vessel off the ground.