An equivalent orthotropic membrane finite element (EOMFE) procedure is developed to analyze and design stringer-stiffened skin panels of aircraft structures in the advanced design stage. The formulation preserves the relation between force, temperature and panel strains and enforces compatibility between stringer and skin strains. This element has been implemented in a large-scale aeroelastic design optimization program (ADOP) and verified against models with explicit representation of stringers. An analytical procedure has been developed to calculate the bidirectional critical buckling stresses for stringer-stiffened panels. This approach can consider full interaction of all in-plane loads. However, in order to avoid performing a prohibitive number of buckling analyses in the optimization problem, a buckling criteria is proposed by which the problem of evaluating the buckling stress allowables is decomposed into three basic types; longitudinal, lateral and in-plane shear. These basic problems are solved analytically based on a finite Fourier series representation of buckling displacement. The analytical procedure was verified against FE models with explicit representation of the stringers. The fully-stressed design (FSD) algorithm in ADOP was modified so that it handles the variation of the stress allowables with the skin thickness and stringer stiffening ratio in each sizing iteration. The EOMFE allows significant flexibility in parametric studies of stringer direction, spacing, and stiffening ratios in the strength and flutter optimization of complex aircraft structures. The bidirectional buckling algorithm will also be implemented in a simultaneous strength/flutter design optimization (SS/FDO) procedure in ADOP to optimize the skin thicknesses and stiffening ratios simultaneously subject to bidirectional buckling constraints. The above approach can be considered local panel optimization combined with a global optimization analysis.