A cylindrical device was analyzed using a Laplace transform-based method. The two-dimensional model represented a pharmaceutical agent uniformly distributed in a polymeric matrix surrounded by an impermeable layer. Molecules could be transferred only through a small hole centered at the top surface of the cylinder. A closed-form solution was obtained to help study the effects of design parameters and geometries on the cumulative amount of drug released. The latter variable increased with the mass transfer and diffusion coefficients and decreased with any increment in the device's length. The delivery rate was described by an effective time constant calculated from Laplace transforms. Reducing the orifice diameter or fabricating a longer system would delay transport of the medication. Simplified expressions for the release profile and the time constant were derived for special design cases.