Abstract The paper considers the problem of design optimization of the box section of the single-girder bridge crane. Reduction of the girder mass is set as the objective function. The algorithm of generalized reduced gradient (GRG2 algorithm) was used as the methodology for determination of optimum geometrical parameters of the box section. The criteria of permissible stresses, local stability of plates, lateral stability of the girder, static deflection, dynamic stiffness and production feasibility (distance between the webs) were applied as the constraint functions. The optimization of the box section geometrical parameters was conducted for payloads and spans typical for single-girder bridge cranes.