The present investigation is devoted to a development of new optimal design concepts of aircraft lateral wing upper covers made of advanced composite materials. In the second part a stiffened composite panel with the best weight/design performance obtained from the linear buckling analysis (Part I) is verified by the nonlinear buckling analysis and re-optimized in the case of necessity. Additionally an effect of shear and fuel pressure as well as an effect of skin post-buckling on its performance is investigated. Three rib bays laminated composite panels with HAT-stiffeners were modeled with ANSYS finite element code to study their buckling behavior as a function of skin and stiffener lay-ups, stiffener height, stiffener top and root width. Due to the large dimension of numerical problems to be solved, an optimization methodology was developed employing the method of experimental design and response surface technique. Weight optimization problems were solved for four load levels, taking into account manufacturing, repairability and damage tolerance requirements. Optimal results were verified successfully using ANSYS shared-node model.