Abstract: In order to simplify the calculations in structural analysis, it is often assumed that some members or their specific directions are rigid. The internal force calculations of the structure with rigid members are difficult points in teaching the structural mechanics. For the sidesway frame containing an inclined bar and a rigid bar, its node displacements will be limited, with the non-independent node displacements. This paper uses the constraint equations of the rigid bars to obtain the coefficient matrix. And based on the rank of the coefficient matrix, the basic unknown of the structure could be determined. Furthermore, the relationships between the independent node displacements and the non-independent node displacements of the structure are derived, so the internal force of the frame could be solved using the displacement method.