This paper examines the problem of the nonreactive advective transport of a contaminant that is introduced at the boundary of a three-dimensional cavity contained in a fluid-saturated nondeformable porous medium of infinite extent. The advective Darcy flow is caused by a hydraulic potential maintained at a constant value at the boundary of the three-dimensional cavity. In order to develop a generalized solution to the problem the three-dimensional cavity region is modeled as having either a prolate or an oblate shape. Analytical results are developed for the time- and space-dependent distribution of contaminant concentration in the porous medium, which can also exhibit natural attenuation. The exact closed-form analytical results are also capable of providing solutions to advective transport problems related to spherical, flat disc-shaped and elongated needle-shaped cavities.