A cylindrical coordinate mathematical model to calculate 222rn flux and movement was developed considering 222rn production, decay, and diffusion in a multilayered, porous, permeable matrix. Air movement, transporting radon through the media, satisfies darcy's law and is influenced by the air (barometric) pressures applied at the surface. Two zones of porous material have been defined, one with 222rn production term (the uranium ore zone) and the other without this term to simulate shotcrete or concrete ground support. A provision is made to evaluate the effect of a pinhole in an otherwise impermeable sealant. Comparisons are made between field measurements and predicted values. Specific examples are given of 222rn losses through pinholes for cases of linearly varying and static barometric pressures. The results suggest factors to consider in uranium mine radon control. For example, pinholes are not a serious problem since it appears that several thousand 2-mm- diam pinholes per square meter are required to cause a significant loss of a barrier coating's effectiveness.