Large-scale numerical computations associated with rock mechanics problems have required efficient and economical models for predicting temperature, stress, failure, and deformed structural configuration under various loading conditions. To meet this requirement, the complex dependence of the properties of geological materials on the time and temperature is modified to yield a reduced time scale as a function of time and temperature under the thermorheologically simple material (TSM) postulate. The thermorheologically linear concept is adopted in the finite element formulation by uncoupling thermal and mechanical responses. The thermal responses, based on transient heat conduction or convective-diffusion, are formulated by using the two-point recurrence scheme and the upwinding scheme, respectively. An incremental solution procedure with the implicit time stepping scheme is proposed for the solution of the thermoviscoelastic response. The proposed thermoviscoelastic solution algorithm is based on the uniaxial creep experimental data and the corresponding temperature shift functions, and is intended to minimize computational efforts by allowing large time step size with stable solutions. A thermoelastic fracture formulation is also presented by introducing the degenerate quadratic isoparametric singular element for the thermally-induced line crack problems. The stress intensity factors are computed by use of the displacement method. Efficiency of the presented formulation and …