In the case of horizontally curved highway bridges, girders are subjected to the combined action of vertical bending and torsion due to the offset. Although steel/concrete composite sections are proportioned to avoid abrupt brittle failure, the ultimate strengths of composite box girders subjected to bending and torsion may be limited by the diagonal tensile stress in the deck concrete induced by the St. Venant torsion. Concurrent compressive stresses in the concrete deck improve the shear resisting capacity of concrete, thereby resulting in increased torsional resistance of the composite box girder in positive bending. Three-dimensional finite element analyses and classical strength of materials investigations were conducted in this study to determine the ultimate strengths of composite box girders in bending and torsion and their interaction. An advanced material model including the concrete tension mechanism was incorporated in the incremental nonlinear analyses. The ultimate strengths from numerical data were compared with theoretically derived values. The proposed interaction equation is very simple, yet it provides a rational lower bound for the determination of the ultimate strengths of concrete/steel composite box girders.