An analytical solution is developed which provides a three-dimensional solution for the fate and transport of contaminants in a variable velocity and axially symmetric flow field. Due to the axially symmetric nature of the flow field, the equations which describe the transport process can be written in two space dimensions, r and z. The solution allows a first-order decay process and linear retardation of the contaminant and assumes that the aquifer is homogeneous and isotropic. Two solution techniques are used and approximate early and late time solutions are presented. The analytical solution is illustrated by several examples using three different boundary conditions at the well.