Abstract The objective of this paper is to investigate the equations of vortex motion (Rectilinear vortices) of fluids. The dissertation is done by considering two-dimensional vortex flow using complex potential. Equations of motions of stream lines and their velocities due to a rectilinear vortex filament in plane, vortex pair, outside a cylinder, inside a cylinder as well vortex rows and Karman vortex street are presented.