Thermoelasticity play pivotal role in the development of science and technology especially aerospace engineering. The present volume entitled "Mathematical Thermoelastic Methods for Physics and Engineering" contains a collection of eleven chapters. The papers are devoted to topics in thermoelasticity. Most of them were published before in journal of international or national repute. To understand this book one must have knowledge of Residue Theory, Differential Equation, Analysis, Integral Transform and Thermoelasticity. The investigations in the present study are based on the research works of Sirakowski and Sun, Roychoudhury, Patel, Tonigawa and Komatsubara, Wankhede, Khobragade and Deshmukh K.C where they have studied the direct and inverse problems of thermoelasticity. Direct problems have applications in the field of Aeronautic whereas inverse problems are very important in view of its relevance to various industrial machines subjected to heating such as main shaft of lathe, turbine and roll of rolling mill. It is also useful to analyze the experimental data and measurement of aerodynamic heating.