In this paper,a finite element method(FEM)-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed.A program of FEM named as SOFT,adopting unified field equations for thermo-hydro-mechanical-air(THMA)behavior of geomaterial and using finite element-finite difference(FE-FD) scheme for soil-water-air three-phase coupling problem,is used in the numerical simulation.As an application of the newly proposed numerical method,two engineering problems,one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste(HLRW),are simulated.The model tests on slope failure in unsaturated Shirasu ground,carried out by Kitamura et al.(2007),is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature.While the in situ heating test reported by Munoz(2006) is simulated in the same framework under the conditions of variable temperature but constant air pressure. In this paper, a finite element method (FEM) -based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated / unsaturated geomaterial is discussed. A program of FEM named as SOFT, governing uniform field equations for thermo-hydro -mechanical-air (THMA) behavior of geomaterial and using finite element-finite difference (FE-FD) scheme for soil-water-air three-phase coupling problem, is used in the numerical simulation. As of application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste (HLRW), are simulated. model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. (2007), is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. Whilst the in situ heating test was reported by Munoz (2006) is simulated in the same framework under the conditions of variable temperature but constant air pressure.