Abstract A widely held view is that cytoplasmic streaming is propelled by structural changes in the macromolecules within the cytoplasm. In a continuum theory this would be represented as a system of body forces which would not in general be irrotational. This paper develops numerical methods for investigating creeping flow driven by body forces in a cellular geometry which currently attracts much interest, viz. the nerve fiber. The methods, however, have more general applicability. In particular, they mesh well with a technique which has already proved useful for analytic investigation of flows of slightly non-Newtonian fluids.