In the course of time, the study of vibration of plates with thickness variability has acquired great importance in nuclear reactor technology, earth-quake resistant structures, aeronautical field, naval structures and machine designs etc. Plates of variable thickness are mainly used for two fold requirements of safety and economy. Therefore, it becomes the need of the hour to provide some authentic theoretical mathematical models for the help of mechanical/design engineers & scientists so that before finalizing any design or mechanical structure, they can use of them with practical approach and provide much better design and structures with more durability, reliability & strength. In the present work, some mathematical models on vibrational behaviour of visco-elastic homogeneous rectangular plates with bi-directional thickness variability are deeply discussed for fixed boundary conditions. Numeric values of time period, deflection and logarithmic decrement are given in tabular and graphical forms both. I hope that the engineers/scientists may develop a qualitative understanding of plate vibrational behaviour by using these findings.