A combustion model has been formulated to solve the burning rate eigenvalue problem for a model heterogeneous solid propellant (two-dimensional sandwich) with Peclet number of O(1), similar to what has been done previously for homogeneous energetic solids. A two-step reaction sequence (high-activation-energy, condensed-phase decomposition followed by low-activation-energy, gas-phase heat release) has been extended from one to two dimensions for nonpremixed (heterogeneous fuel/oxidizer) composite solids. Gas-phase streamwise diffusion, the primary driving force for solid pyrolysis, has been accounted for by including a finite value of the Peclet number. The results show that the value of the Peclet number, a nondimensional burning rate, is constrained to a reasonably small interval by the eigenvalue expression obtained from activation energy asymptotic analysis of the condensed-phase thermal decomposition zone. These results demonstrate the feasibility of and general approach for solving the two-dimensional composite propellant burning rate as an eigenvalue problem. (C) 2000 by The Combustion Institute.