This paper presents a Buckley-Leverett analytical solution for non-Darcy displacement of two immiscible fluids in porous media. The multiphase non-Darcy displacement is described using a Forchheimer equation or other non-Darcy flow correlations under multiphase flow conditions. The analytical solution is used to obtain some insight into the physics of displacement involving non-Darcy flow effects in porous media. The solution reveals how non-Darcy displacement is controlled not only by relative permeability curves but also by non-Darcy flow coefficients as well as injection or flow rates. This analytical solution is then applied to verify a numerical simulator for modeling multiphase non-Darcy flow. ¿ 2001 American Geophysical Union