Abstract: Mass matrix and stiffness matrix of semi-rigid frames fordynamic finite element analysis are deduced．Multistory frames with semi-rigidconnections of different initial stiffness are constructed together with thecorresponding rigid frame. Finite element analysis software ANSYS is used toperform the numerical analysis. The influence of connection stiffness on naturalfrequencies of structures is analyzed. The response of different framesaccording to harmonic loading with different frequencies is studied.Further,by adopting a time--dependent method, structures under excitation of seismicwaves are analyzed. Analysis results show that the connectionflexibility has agreat effect on structure's natural frequencies. The naturalfrequency decreases with the increase of connection flexibility. It isnecessary to consider theconnection flexibility in the seismic design of steel structures. Timecurvesof top point lateral displacement and column base shearing force ofsemi-rigid frames behave stably during the excitation time. Flexibleconnections can be used instead of rigid connections in seismic design ofsteel frames.