Double skin composite (DSC) panels are constructed by filling concrete between two steel plates welded with stud shear connectors at a regular spacing. Steel plates in DSC panels used as two-way slabs or shearwalls may buckle locally between stud shear connectors when subjected to in-plane biaxial compression. This paper investigates the local and post-local buckling behaviour of biaxially compressed steel plates restrained by shear connectors and concrete in DSC panels by using the finite element modelling technique. Local buckling coefficients are obtained for steel plates with various aspect ratios, biaxial loading and boundary conditions by incorporating the shear stiffness effect of stud shear connectors. These buckling coefficients can be used to determine limiting width-to-thickness ratios for steel plates and the distribution of stud shear connectors. A geometric and material non-linear analysis is undertaken to quantify the post-local buckling strength of steel plates under biaxial compression. The initial imperfections of steel plates and non-linear shear–slip characteristics of stud shear connectors are taken into account in the post-local buckling analysis. Based on numerical results, biaxial strength interaction curves and formulae are developed for the ultimate strength design of steel plates in double skin composite construction.