In the modern epoch of science and technology; scientists, engineers & practitioners have become more interested to analyze the vibrational characteristics of structural components which are mainly operated under elevated temperature i.e. space technology, nuclear energy applications, high speed atmospheric flights etc. Due to the influence of temperature, the physical properties of materials change significantly. Further, the use of various plate type structural elements under high temperature environments, particularly in space vehicles and modern missiles, demand that non-homogeneity of the material should be taken into account to predict their natural frequencies. The book is mainly the collection of theoretical mathematical models about the effect of bi-dimensional temperature variations on vibrations of four sided clamped square plate with bi-dimensional thickness variability. Numeric values of natural frequencies are calculated for both the modes of vibrations for different values of taper parameters & thermal gradient. We hope that the content of the book will definitely help the readers as well scientists to fulfill their requirements.