The aims of this work are three: First, to make a brief review of linear system and estimation theory used in mechanical structure problems. Second, to study an algorithm called ERA (Eigensystem Realization Algorithm) that provides a minimal realization using the input (forces, moments, impulses) and output signals (accelerations). Third, to develop some numerical and experimental applications. To achieve these goals, a study of deterministic and stochastic linear systems is performed in order to provide some basic insights. In the same way, characteristics and properties of the Bayesian, maximum likelihood and least square estimators are presented. With this background, the original ERA and an alternative algorithm called ERA/OKID (Observer Kalman Filter Identification) are described. Since the use of an observer gives a system a statistical framework that allows the estimators to deal with noise, the behavior of ERA and ERA/OKID when applied to a bidimensional truss a®ected by di®erent levels of noise is studied . The last part of this work is concerned with the applications. That consist of an experimental and a numerical part: In the first part, two sets of data are generated by performing two experiments. In each one, a tridimensional truss was excited by a randomic force and the accelerations of two points of the structure were measured. With one set of data, it is found a state space model of minimal order using ERA and ERA/OKID. Comparisons are made between the output signals generated by the identified model and the real truss for each input signal. The goal is to achieve a state space model of minimal order without performing any mathematical model process. In the second part, it is performed an application of the RSS (Remote Sensor System) algorithm using a damped mass-spring system. This algorithm, proposed in [42] is famous because it was used to identify whether the MIR space station was damaged after a docking process. In the identification stage of the RSS algorithm, ERA and ERA/OKID is used.