Discrete vortex methods have been developed to investigate the vortex flows on cones and two-dimensional cylinders. The cone problem was solved by assuming that, to meet conical flow and zero-force conditions, the vortices move radially away from the body at a given cross-section. The two-dimensional cylinder problem was solved by limiting the velocity along the zero streamline surrounding the vortex field to two times freestream velocity and by limiting the lateral movement of the vortices. Variations in vortex position and strength with time were determined by taking into account the rate at which circulation is generated at separation points on the body. The calculated vortex positions and strengths were in good agreement with available experimental data. Viscous effects could be accounted for by adding empirically determined damping terms to the velocity equations. The models indicate that different types of asymmetry occur for the cone and two-dimensional cylinder. Asymmetry onset boundaries determined by the discrete vortex method show the same trend as experiment.