Monte Carlo techniques were used to evaluate the flow of molecules through an ideal orifice (effusion) as predicted by isotropy-failure theory. Binary collisions of molecules were treated using classical mechanics with random numbers used for molecular speeds, directions, and recoil angles. Isotropy-failure theory was applied to give the dependence on pressure of the gas. Isotropy-failure theory assumes that the probability of escape is increased by the absence of the container wall where the orifice is located. The simulation was performed for Ar at 1000 K for 10(7) collisions. The simulation provided the number of molecules and their speeds in the orifice direction as a function of the isotropy-failure parameter domega/2pi (related to the Knudsen number defined as the mean-free path divided by orifice diameter). As domega/2pi increased (Knudsen number decreased, pressure increased) the transmission probability of the orifice increased, and the average speed of molecules escaping along the orifice normal increased. The results are compared to experimental results for the orifice transmission probability and speed distribution.