The mass transport problem from a Newtonian fluid to a swarm of prolate and/or oblate spheroidal adsorbers under creeping flow conditions is considered here. The spheroidal-incell model is used for the analytical description of the flow field within the swarm. The convective diffusion equation along with the appropriate boundary conditions for the description of the adsorption upon the solid surface is solved analytically for high Peclet numbers and numerically in the low Peclet regime. In both cases, analytical expressions for the adsorption rate are obtained. It is found that the oblate geometry offers significant advantage for capturing the diluted mass compared with the prolate one even in strongly convective environments. It is also shown that the assumption of instantaneous adsorption overestimates significantly the adsorption efficiency.