The dynamic behavior of plates with mixed boundary conditions has been the subject of intensive study for many years due to its great importance in many engineering applications. On-trend approach in dynamic response analysis is to combine mathematical model, test results and computer simulation. Classical techniques of mathematical modeling of intricate structural systems for response analysis in frequency or time domain are tiresome and time consuming. In this study, a point supported rectangular plate considered and extraction of its system model from FE model, validated by the test results, by using commercially available computer programs such as Ansys and Mat lab is demonstrated. State space mathematical model in principal coordinates obtained in Mat lab from the modal analysis results of its FE model. Its modes sorted with respect to peak gain values, and the modes with the less contributions to the response truncated. To validate the accuracy of this method and truncation, transient responses from the full model with no reduction, truncated model, and Ansys are compared and found to be in accord with each other. It's demonstrated by plotting the indicated results of analyses, and emphasized the significant processing times between the conventional approach and stated method. It is concluded obvious that this study will make a good understanding in simplifying the dynamic analysis of vibration problems of plates.