A numerical solution is given for nonlinear optical wave-guides with power confinement in both transverse dimensions. Self-consistent solutions are obtained by using an accurate vector finite element formulation along with the penalty technique. Numerical results for the first quasi-TM power-dependent mode are presented for strip-loaded waveguides with saturable self-focusing media. The variations with total power are illustrated for the modal index and for the fraction of the total power carried by different regions, showing interesting abrupt power switching for realistic geometries.