In this chapter, we describe the conservation equations and assumptions that govern the behavior of opposed-flow and stagnation flames, which may result from impinging separate fuel and oxidizer streams or from two premixed streams, or from a premixed stream impinging on a solid surface. The governing equations rely on a similarity transformation that reduces the three-dimensional nature of the flow to a one-dimensional (axial) dependence of the governing equations. This discussion pertains to the Ansys Chemkin Reactor Models: Diffusion or Premixed Opposed-flow Flame and Premixed Burner-Stabilized Stagnation Flame.