The paper describes the development of a new hybrid computational approach for nonlinear/linear thermal-structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements with transform methods and the classical Bubnov-Galerkin schemes. Application of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capabilities of the proposed hybrid transfmite element methodology.