The widespread use of thin-walled composite structures in weight-critical applications such as aircraft and spacecraft require a comprehensive understanding of their stability behavior. Therefore, a new computational model is proposed to provide an efficient method for the local buckling and postbuckling analysis of omega-stringer stiffened panels under uniaxial compression. Closed-form analytical solutions are derived based on the principle of the minimum of the total elastic potential and approximate the postbuckling behaviour near the bifurcation point. The solution assumes that the initial eigenform does not substantially change in the early postbuckling regime. The stiffened panel under consideration consists of the skin plate with eccentrically attached stringer feet along the longitudinal sides of the panel, while the remaining part of the omega-stringer is modeled by corresponding elastically restrained edges. The new analysis method is assessed through a comparison with finite element analysis. Compared to numerical methods, the present model promises to be a highly efficient tool in the preliminary design framework.