A complete mathematical model of the Rice University shaking table facility is developed. The analytical model, developed on the basis of previous work, is then fully developed in order to account for: Proportional, Integral, Derivative, Feed-Forward and delta-Pressure controls, for servovalve response delay, for flexibility of the foundation, for flexible MDOF test specimen. The mathematical model is then used in order to gain insight into the dynamic performance of the shaking table and its sensitivity to the various control gain parameters. Furthermore, the mathematical model is used to determine the influence of the dynamic properties of the test specimen on the shaking table performance. These analyses are fundamental in order to tune the shaking table and in order to understand the capacities and limits of the shaking table. Comparison with experimental results shows that the mathematical model developed can predict very accurately the actual table performance.