Most of stiffened panels subjected to bi-axial compression mainly in transverse direction collapse with the buckling deformation of one times one half-wave in a local panel between longitudinal stiffeners and transverse frames. The authors defined this collapse mode as "local panel buckling mode". In this study, the collapse behavior of the stiffened panel with local panel buckling mode is investigated in detail. Then, a simple design formula to estimate ultimate strength of a stiffened panel with local panel buckling mode is derived based on the collapse behavior. This formula is composed of a formula to predict the ultimate strength of a rectangular unstiffened panel subjected to uniaxial transverse compression, and the effects of stiffeners, bi-axial compression and von Mises yield condition are added to the formula. The ultimate strength calculated by the proposed formula is in good agreement with FEA results. Finally, the proposed formula is compared with an existing method and formulae used in the CSR-OT, CSR-BC and H-CSR. As a result, it is confirmed that the proposed formula has sufficient accuracy and high availability.