The diffusion rate of a spherical drug delivery device was analyzed using a Laplace transform-based method. The three-dimensional model represented a pharmaceutical agent distributed, not uniformly, in a polymeric matrix. Molecules could only be transferred to the outside of the matrix through a thin spherical sector of the device. A closed-form solution was obtained to help study the effects of diffusivity parameters and geometries on the cumulative amount of drug released. The latter variable increased with the mass transfer and diffusion function and decreased with any increment in the device's length. The solution obtained was in terms of the Legendre polynoms, and developed using the Maple software. It is expected that the results presented help to the future design of devices in pharmaceutical engineering.