This work describes the process of mass transfer which takes place when a fluid flows past a soluble surface buried in a packed bed of small inert spherical particles of uniform voidage. The fluid is assumed to have uniform velocity far from the buried surface and different surface geometries are considered; namely, cylinder in cross flow and in flow aligned with the axis, flat surface aligned with the flow and sphere. The differential equations describing fluid flow and mass transfer by advection and diffusion in the interstices of the bed are presented and the method for obtaining their numerical solution is indicated. From the near surface concentration fields, given by the numerical solution, rates of mass transfer from the surface are computed and expressed in the form of a Sherwood number (Sh). The dependence between Sh and the Peclet number for flow past the surface is then established for each of the flow geometries. Finally, equations are derived for the concentration contour surfaces at a large distance from the soluble solids, by substituting the information obtained on mass transfer rates in the equation describing solute spreading in uniform flow past a point (or line) source.