This paper deals with the realization of finite dimensional, linear, time-invariant models of structural systems in the state space description from the response (output) of the system. The theory and and underlying principles of two stochastic system identification algorithms are first described. The applications of the algorithms to two civil engineering structures follow the theory. Ambient vibration data collected from a building and a bridge, both are permanently instrumented by accelerometer networks, are used to derive the models. The vibration characteristics, i.e., the frequencies, damping ratios, and associated mode shapes, of the structures are then retrieved from the models. The stochastic system identification algorithms prove to be very effective in identifying the vibration characteristics of the structures.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.