A joint experimental and theoretical project has been initiated at Virginia Tech to study the effects of dual-mode combustion at high pressures for a two-dimensional Wolfhard-Parker burner. This thesis is the first stage of the theoretical part of the project, and contains a numerical study of laminar coflow diffusion flames stabilized on a confined Wolfhard-Parker burner. A global finite difference method is used where the nonlinear equations written on a stream function-vorticity formulation are solved with a flame sheet approach. The pseudotransient, approximative factorization method is utilized to solve the coupled system of equations. Adaptive gridding, numerical evaluation of Jacobians and iterations within time step are implemented for computational efficiency. Numerical results have been obtained for different fuels under different conditions. Comparison with measured data by Smyth et al. (1985) for a buoyancy dominated methane-air flame is made. The location of the flame front is accurately predicted. The temperature is over predicted in the fuel rich zone since pyrolysis and radiation effects have not been accounted for in the numerical model. Good agreement is observed for major species and velocities. As expected, large velocity increase and horizontal inflow of nitrogen and combustion products associated with buoyancy occur in the lower region of the flame. / Master of Science