Numerical analysis of local similarity solutions of laminar, free convective flow over a vertical plate with uniform wall temperature and surface heat flux cases in non-Newtonian power law fluids is considered. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a pseudo-similarity variable transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation. Results are obtained for the cases of modified Prandtl numbers, based on the local value of x, of 1, 10, 100, and 1000 over a range of values of the fluid flow index from 0.5 to 1.5. Representative local Nusselt number and average Nusselt number as well as velocity and temperature profiles are presented. Comparisons with earlier works are also made for large modified Prandtl numbers.