Advances in the design of membranes and membrane modules have led to a variety of new configurations with enhanced separation performance. In order to study the performance of membrane systems with novel geometries, the flow field of the continuum phase must be known. In this study an approximate approach is used to obtain the solution for steady state flow fields in several crossflow membrane filtration systems with cylindrical symmetry. The analytical solutions are presented for a single channel tubular membrane, a tubular membrane with a co-axial solid cylinder at its center, a tubular membrane located at the center of a channel with impervious walls, and a configuration with two tubular co-axial membranes. The results are compared to numerical solutions. The analytical solutions for both velocity and pressure distributions are in agreement with the results of numerical modeling.