With an ongoing desire to improve product performance, in combination with the continuously growing complexity of engineering structures, there is a need for well-tested and reliable engineering tools that can aid the decision making and facilitate an efficient and effective product development. The technical assessment of the dynamic characteristics of mechanical systems often relies on linear analysis techniques which are well developed and generally accepted. However, sometimes the errors due to linearization are too large to be acceptable, making it necessary to take nonlinear effects into account. Many existing analysis techniques for nonlinear mechanical systems build on the assumption that the input excitation of the system is periodic and deterministic. This often results in highly inefficient analysis procedures when nonlinear mechanical systems are studied in a non-deterministic environment where the excitation of the system is stochastic. The aim of this thesis is to develop and validate new efficient analysis methods for the theoretical and experimental study of nonlinear mechanical systems under stochastic excitation, with emphasis on two specific problem areas; forced response simulation and system identification from measurement data. A fundamental concept in the presented methodology is to model the nonlinearities as external forces acting on an underlying linear system, and thereby making it possible to use much of the linear theories for simulation and identification. The developed simulation methods utilize a digital filter to achieve a stable and condensed representation of the linear subparts of the system which is then solved recursively at each time step together with the counteracting nonlinear forces. The result is computationally efficient simulation routines, which are particularly suitable for performance predictions when the input excitation consist of long segments of discrete data representing a realization of the stochastic excitation of the system. Similarly, the presented identification methods take advantage of linear Multiple-Input-Multiple-Output theories for random data by using the measured responses to create artificial inputs which can separate the linear system from the nonlinear parameters. The developed methods have been tested with extensive numerical simulations and with experimental test rigs with promising results. Furthermore, an industrial case study of a wave energy converter, with nonlinear characteristics, has been carried out and an analysis procedure capable of evaluating the performance of the system in non-deterministic ocean waves is presented.