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A numerical and experimental study of time domain methods for modeling and parameter identification of structural systems is presented. Models are developed which can be used to predict the transient response of multiple- degree-of-freedom systems subjected to arbitrary input. The linear, discrete time transfer function is expressed in a form called the Autoregressive Moving Average (ARMA) model. The ARMA model is a minimum parameter model that may be parameterized with a minimum number of measured quantities. The ARMA model is contrasted to traditional models such as differential equation models and modal methods. The ARMA model indentification algorithms are also compared to time domain modal methods. Though it has proven useful for a number of low-order systems, the identification of the ARMA model is often hampered by the sensitivity of parameter estimates to measurement noise bias.