A pressure-based, unstructured finite volume method has been applied to couple the chemical kinetics and fluid dynamics and to capture effectively and accurately the steep gradient flame field. The pressure-velocity coupling is handled by two methodologies including the pressure-correction algorithm and the projection scheme. A stiff, operator-split projection scheme for the detailed nonequilibrium chemistry has been employed to treat the stiff reaction source terms. The conservative form of the governing equations are integrated over a cell-centered control volume with collocated storage for all transport variables. Computations using detailed chemistry and variable transport properties were performed for two laminar reacting flows: a counterflow hydrogen-air diffusion flame and a lifted methane-air triple flame. Numerical results favorably agree with measurements in terms of the detailed flame structure.