Steel plates in double skin composite (DSC) panels are restrained by a concrete core and welded stud shear connectors at discrete positions. Local buckling of steel plates in DSC panels may occur in a unilateral mode between stud shear connectors when subjected to combined states of stresses. This paper studies the local and postlocal buckling strength of steel plates in DSC panels under biaxial compression and in-plane shear by using the finite element method. Critical local buckling interaction relationships are presented for steel plates with various boundary conditions that include the shear stiffness effects of stud shear connectors. A geometric and material nonlinear analysis is employed to investigate the postlocal buckling interaction strength of steel plates in biaxial compression and shear. The initial imperfections of steel plates, material yielding, and the nonlinear shear–slip behavior of stud shear connectors are considered in the nonlinear analysis. Design models for critical buckling and ultimate strength interactions are proposed for determining the maximum stud spacing and ultimate strength of steel plates in DSC panels.