This book contains mathematical concepts and theories on topic of thermo elasticity. The concept of thermo elasticity which forms the central theme of this book, finds its roots and application in branches of Mathematics, Physics and Engineering. Thermoplastic behavior of different geometric structures and different boundary conditions are discussed in depth for better understanding of the topics. The mathematical approach for thermoplastic problems may be of immense help for those students, researchers and teachers pursuing work on thermo elasticity and will be helpful to increase the thermal efficiency of materials. The book contains Thermoelastic Damped Vibration Analysis in A Thick Plate Subjected to Time-Dependent Rectangular Frame Sectional Heat Supply , Thermoelastic Vibrations Analysis of A Thin Isotropic Solid Elliptic Cross Section, An Integral Transform for A Gaussian Hypergeometric Differential Equation Amidst Conditions of Radiation Type Contour, Thermoelastic Analysis of A Functionally Graded Hollow Cylinder Under Electro-Thermo-Mechanical Loads, etc.