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 first part three rib bays laminated composite panels with T, I and HAT-stiffeners were modeled with ANSYS and NASTRAN finite element codes to investigate 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 and large number of optimization tasks to be solved, an optimization methodology was developed employing the method of experimental design, response surface technique and linear buckling analysis. Weight optimization problems were solved for the laminated composite panels with three types of stiffeners, two stiffener pitches and four load levels taking into account manufacturing, repairability and damage tolerance requirements. The composite panel with the best stiffener type was identified for the subsequent nonlinear buckling analysis and optimization presented in the Part II.Optimal results were verified successfully using ANSYS shared-node and NASTRAN rigid-linked models.