The approximate analytical and numerical solutions of the problem of aerosol motion in a circular hole inside a porous medium are presented using the approximations of Poiseuille flow for the carrier phase and the convective-diffusive equation of transport of inertialess particles. Analytical expressions for the fluid velocity profile, the space distribution of particle concentration, and the penetration that include the Darcy number and a slip coefficient at the interface between the porous medium and an adjacent free fluid are obtained as parameters. The numerical solution of the problem of the air flow in the combined porous and free fluid regions was used in order to find the relation between the slip coefficient and the Darcy number.