In this work, boundary layer development was investigated for a mass transfer process between a moving fluid and a slightly soluble cylinder or plane surface buried in a packed bed, in alignment with the direction of flow. The bed of inert particles is taken to have uniform voidage. For this purpose, numerical solutions of the partial differential equations describing mass concentration of the solute were undertaken to obtain the concentration boundary layer thickness as a function of the relevant parameters. Mathematical expressions that relate the dependence with the Peclet number and aspect ratio of the immersed active surfaces are proposed to describe the approximate size of the concentration boundary layer thickness.