This paper is concerned with the development of a finite element method for the elasto-plastic analysis of a gas turbine wheel under severe thermal and mechanical loads. A computer program based upon this development has been written and checked by running sample problems for which the solutions exist in the literature. The output of the computer program gives the transient displacements and stresses for a specified set of discrete points in the structure. As an illustration of an actual application, one power turbine wheel has been analyzed by using the developed method and running the checked computer program. The method developed in this paper should serve as a useful tool in turbine wheel design and should result in improved wheel designs and extended engine durability.