The hybrid space propulsion classically employs a liquid (or gaseous) oxidizer injected into the combustion chamber which contains the solid reducer. The diffusion flame, which appears at the confluence of the oxidizer and reducer mater fluxes, is auto-entertained by the fuel pyrolysis piloted by the heat which is provided to it by the combustion. In order to increase performances of this propulsion system, it is necessary to well understand the coupling effect of the physical and chemical phenomena. The propellants couple polyethylene/gaseous oxygen and nitrogen mixture has been chosen for this study. Properties of the polyethylene have been determined by several chemical analyses, showing that there are a pressure and atmosphere nature effects on the pyrolysis chemical composition. A test bench with instrumentation allowed to characterize the behavior of the polyethylene in real situation. Data acquired have been analyzed in order to obtain physical variables relevant for comparing the numerical simulations results. To undertake simulation of the combustion chamber of hybrid rocket, a new numerical model has been developed. Numerous "academic" test cases are presented and confirmed a good implementation of the numerical method and of the physical and chemical models. Nevertheless, during simulations of hybrid combustion chamber, a pressure divergence has appeared thus causes have been actively investigated.