An analytical Investigation is made of the dynamic response of multi-degree-of-freedom shear beam type buildings excited by transient lateral motions of the base. The response quantities studied are the horizontal displacements of stories relative to the base, the interfloor deformations, the shear forces and induced overturning moments at the story levels. The contribution of the various natural modes of vibration to the response is extensively examined. A representative stiffness distribution is chosen for buildings with constant story masses and a wide range of fundamental frequencies considered. The input notions taken are piece-wise linear; a standard simple pulse and en earthquake motion wore selected for this study. The dependence of response quantities on the fundamental frequency of these structures is examined on as to provide a basis for anticipating the behavior which may be expected. The results are graphically summarized.