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.