A kinetic model for molecular flow is developed to simulate the escape rate profiles that result when molecules are pulsed into the top of a cylindrical tube, experience non-reactive collisions with the tube surface and are detected after exiting at the base. The model includes time-dependent rate coefficients for formation of a pseudo steady-state spatial distribution and for escape. The mean distance traveled down the tube per collision is estimated by applying a cosine directional distribution. Under molecular flow conditions and for non-sticky gas/surface interactions this model allows for the determination of the average number of collisions per molecule before detection. Simulations were carried out on SF6, Ar, N2, Ne, He colliding with Pyrex and Teflon-coated surfaces at temperatures ranging from 25 to 64 °C and in tubes with a range of dimensions. Mean collision numbers are in agreement with those calculated from Monte Carlo simulations.