A method by which the system parameter matrices can be estimated from measured time data of excitation force and acceleration has been studied. The acceleration data are integrated numerically to obtain the velocities and displacements, and the systm parameters are estimated from these data by solving equations of motion. The characteristics of the method have been investigated through its application to simulated data of 1 DOF and 2 DOF systems and experimental data measured from a simple structure. It was found that the method is very sensitive to measurement noise and the accuracy of the estimated parameters can be improved by averaging the repeatedly measured data and removing the noise. One of the main advantages of the parameter estimation method is that no a priori information about the system under test is required. The method can be easily extended to non-linear parameter estimation.