A new model problem in which fuel and oxidizer enter the reaction zone in mutually perpendicular directions is formulated in order to understand the process of flame-positional stability. In the present paper, an analytical formulation valid at the limit of constant density and infinitely fast chemistry is used to obtain solutions in the convective and diffusive limits. A full numerical simulation in which the compressible reacting flow equations are solved for one-step, finite-rate chemistry is utilized to examine the effects of stoichiometry, reactant velocities, and preheating on laminar flame location and structure. The effect of increased fuel velocities and reduced stoichiometric mixture fraction is to bring the flame zone closer to the oxidizer surface, consistent with the simplified analytical predictions and previously reported experimental observations. This corner flame has some of the characteristics of both a classical premixed and a diffusion flame. Under certain conditions, it has the structure of an edge flame. Numerical simulations of a simplified form of the thermodiffusive equations, with the same kinetic scheme yield similar overall results. However, there are qualitative and quantitative differences, which are attributed to simplifications employed.