A numerical approach based on the finite element method is developed for the analysis of lossy nonlinear optical waves guided by planar nonlinear waveguiding structures containing arbitrary lossy materials. In this approach, the power-dependent complex propagation constants and the local electromagnetic field distributions, for both TE and TM waves, are obtained directly from the given lossy nonlinear waveguides. In particular, for the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. The power-dependent complex dispersion relations for TE and TM waves in a lossy nonlinear guiding system with a wide range of absorption coefficients are simulated and analyzed. It is shown that the complex dispersion relations, for both TE and TM waves, are strongly power dependent and most importantly, the bistability phenomena will no longer exist if the absorptive loss is high enough.