Effective and efficient system identification techniques for discrete, time domain, linear, MIMO, heavily damped modal systems from input/output sequences have been developed and simulated. This will facilitate a better understanding of the possible errors in the estimated model and lead to a more accurate compensator and estimator design. Three different time domain system identification algorithms have been developed in this work. The first algorithm determines the state space model in a pseudo controllable/observable canonical form. The second method is a computational simplification of the Eigensystem Realization Algorithm using pseudo observability and controllability indices. The third algorithm tested is the Pseudo Linear Identification Algorithm (PLID). The PLID algorithm is extensively tested on simulated data. This algorithm is also applied to identify a rectangular plate which gives a realistic idea of the identification capabilities of the PLID algorithm to real measured data.