In many supercell simulations, near-ground vortex formation results from the collapse of an elongated region of enhanced vertical vorticity. In this study, this ‘‘roll-up’’ mechanism is analyzed by investigating the behavior of several 2D elliptic vortex patches. The problem is treated as a nonlinear initial value problem, which is better suited to describe the roll-up mechanism than the more commonly employed normal-mode analysis. Using the Bryan Cloud Model 1, it is demonstrated that the condition for vortex formation is an initial finite-amplitude nonuniformity within the vortex patch. Vortex formation results from differential self-advection due to the flow induced by the patch itself. Background straining motion may either aid or suppress vortex-patch axisymmetrization depending on the initial orientation of the patch relative to the deformation axis. It is also found that in some cases numerical dispersion may lead to nonuniformities that serve as seed for axisymmetrization, thus resulting in unphysical vortex development.