The velocity of a fluid mass imbedded in another fluid, which is of a different viscosity and a different specific weight and flowing in a porous medium under a prevailing uniform pressure gradient, is investigated. The fluid mass may take the form of a circular or elliptic cylinder, a sphere, or an ellipsoid, and the orientation of the fluid mass, if not spherical, is completely arbitrary with respect to both the direction of the pressure gradient and that of gravity. Exact closed solutions are obtained. The results for two‐dimensional flows are applicable to Hele‐Shaw cells.