The problem of mass transfer from a Newtonian fluid to a swarm of spheroidal adsorbers under creeping flow conditions is considered using the spheroid-in-cell model to represent the swarm. The flow field within the fluid envelope for the Kuwabara type of boundary conditions is obtained form the analytical solution of Dassios et al. (1994). The complete convective diffusion equation is used to describe mass transport within the envelope so that moderate and strong diffusional terms can be taken into account. A new set of boundary conditions is used that respects mass flux and concentration continuity across the outer surface of the cell and maximizes the applicability of the spheroid-in-cell model in the convection-to-diffusion transition regime. The resulting elliptic problem in two dimensions is solved numerically. Results for the upstream and downstream concentration profiles reveal that tangential diffusion is very significant and should not be neglected for moderate and low Peclet number values. Also, the classical Levich-type of formulation, which is theoretically valid for very weak diffusional terms only, can in practice be modified to predict with fair accuracy the overall Sherwood number and the adsorption efficiency of prolate and oblate spheroids-in-cell even in moderate Peclet number cases.