The purpose of this investigation was to determine analytically the molecular incidence rates on the various surfaces of the space simulator. The mathematical model of the space simulator consists of two concentrically located spherical surfaces corresponding to the chamber wall outside and to the vehicle inside. The analysis is divided into two phases. Phase I deals with conditions of uniform pumping and outgassing on each surface. A square pulse of outgassing is assumed to occur and the total number of molecular hits is determined for each surface. These results are extended to a steady state uniform flow and the molecular incidence rates are obtained. Phase II is an analysis of the nonuniform case introduced by surface discontinuities of axiosymmetric type. The procedure followed is to determine the various probabilities that a molecule leaving a surface will hit spherical zones on either surface. Using these probabilities the molecular incidence rates can be determined. While the probabilities have been found, analytic expressions for molecular incidence determination are very difficult to obtain. The problem, therefore, was approached from a computer point of view enabling us to obtain computer solutions with a high degree of accuracy.