The goal of this investigation is to construct a computational procedure for identifying the modal parameters of linear mechanical systems. The methodology employed in the paper is based on the Eigensystem Realization Algorithm implemented in conjunction with the Observer/Kalman Filter Identification method (ERA/OKID). This method represents an effective and efficient system identification numerical procedure based on the time domain. The algorithm developed in this work is tested by means of numerical experiments on a full-car vehicle model. To this end, the modal parameters necessary for the design of active and semi-active suspension systems are obtained for the vehicle system considered as an illustrative example. In order to analyze the performance of the methodology developed in this investigation, the system identification numerical procedure was tested considering two case studies, namely a full state measurement and an incomplete state measurement. As expected, the numerical results found for the identified dynamical model showed a good agreement with the modal parameters of the mechanical system model. Furthermore, numerical results demonstrated that the proposed method has good performance considering a scenario in which the signal-to-noise ratio of the input and output measurements is relatively high. The method developed in this paper can be effectively used for solving important engineering problems such as the design of control systems for road vehicles.