Abstract The continuous mass matrix method has been extended to include the forced vibration in the dynamic analysis of plane and space frameworks. The forcing forces may be continuous of discontinuous functions of time but all the forcing forces acting simultaneously on a framework must have the same time variation in order that the modal analysis can be applied. The damping has been neglected. The concept of code numbers in the case of static loading has been extended to the dynamics of structures. The validity of the two orthogonality conditions of the modal shapes has been proved for the continuous mass matrix method so that the modal analysis could be applied easily. The set of simultaneous equations of motion has been converted to equivalent one-degree-of-freedom systems. In the case where the forcing forces have different time variation functions a numerical analysis can be performed. Illustrative sample problems have been solved and the results are given in tabular form.