Resistive instabilities are unstable modes which disappear as resistivity tends to zero. Their growth time is proportional to a positive fractional power of resistivity. The equilibrium we consider has axial symmetry in a cylinder. With small but finite resistivity these modes originate about a surface, known as a resonant surface. Using the tearing ordering, we develop a system of ordinary differential equations to model the modes, including shear flow. We develop a numerical code to solve the system. We plot the loci of the growth time for increasing flow for a sample of the other parameters. We also plot marginal stability curves. Our results show a strong interaction between flow and some of the other parameters. We also include a couple of series solutions to the problem. One is valid as viscosity tends to infinity and the other as flow tends to infinity.