Abstract: The engineering structure time history response in earthquakes was analyzed by means of state space theory. The state equations of the engineering structure time history responses were established with the inhomogeneous solutions given on the basis of the structure dynamic equations and the state variables. The Kely-Hamilton method, the state space method and the fine integral method were applied with the corresponding computing format and programs to solve the matrix exponential function. Several numerical examples demonstrate that the state space method has better accuracy and higher efficiency for analyzing structures dynamic time history responses.