Numerical code to analyze chemically reacting flows in the solid fuel ramjet engine combustor has been developed. LU-SSOR implicit scheme with finite volume method is used to solve the Navier-Stokes equations fully coupled with the chemical species continuity equations. Polyethylene is used as solid fuel and chemical reactions are modeled by a 6 species,2-step finite chemistry. The turbulence is treated by the Baldwin-Lomax algebraic model. To verify this numerical code, axisymmetric compressible flows in the JPL nozzle and chemically reacting flows over 2-D compression ramped duct are solved. After code verification, the variations of chemicallyreacting flows in the solid fuel ramjet combustor, mean solid fuel regression rate and thrust for the inflow conditions and combustor geometries are investigated.