The mass transport problem from a Newtonian fluid to a swarm of prolate or oblate spheroidal adsorbing particles under creeping flow conditions is considered here. The spheroidal-in-cell model is used for the analytical description of the flow field within the swarm. A realistic adsorption-reaction-desorption mechanism is used to describe the adsorption of mass on the particle surface, instead of the assumption of instantaneous adsorption that has been adopted previously. The convective diffusion equation accompanied by the appropriate boundary conditions is solved analytically for the case of high Peclet numbers and numerically for the low ones. In both cases, analytical expressions for the overall Sherwood number, the adsorption rate, and the mass transport coefficient were obtained. It was found that the adsorption rate is higher for oblate shapes and for diffusional, instead of convectional, environments. Finally, the assumption of instantaneous adsorption leads to values for the overall Sherwood number and the adsorption efficiency that are 15-50% lower and 10-35% higher, respectively, than those obtained by using the more realistic adsorption-reaction-desorption model.