A geometrically and physically nonlinear finite element approach is presented for the analysis of mode-I and mixed-mode free edge delamination in composite laminates which properly accounts for the effects of initial thermal and hygroscopic stresses. A constitutive model based on nonlinear fracture mechanics is used to describe delamination. An orthotropic softening plasticity model is used to determine the initiation and propagation of delamination. Although the orthotropic yield surface is based on stresses, it is proved, that, in combination with a softening type of post-failure response controlled by the fracture toughness, the approach results in a unique and physically realistic solution upon mesh refinement. The results from the nonlinear finite element computations, including predictive analysis, are compared with mode-I and mixed-mode free edge delamination experiments. This comparison shows that the numerical results are within 10% of the experimental data.