It is crucial to ensure that the cement sheaths remain intact in all types of deep well applications subject to high temperatures and high pressures underground. It should be noted, however, that the behaviour of annulus cement sheath is not self-controlled and is governed by the response of steel casing and the surrounding rock formation in such extreme underground conditions. In this study, we investigate the thermomechanical response of wellbore materials in a typical oil well consisting of steel casing, annulus cement sheaths and surrounding rock formations subjected to continuous steam injection. A section of an oil well was simulated by using the COMSOL Multiphysics, a finite element method, using Class G Portland cement as the annulus cement. In two formation scenarios, stiff (carbonate) and compliant (sandstone), temperature and pressure were coupled to evaluate wellbore material behaviour. It was found that wellbore materials in carbonate were more susceptible to stress than those in sandstone. Despite the fact that all materials reached their highest temperatures in both formations, the retention time of the maximum temperature in the cement sheath in sandstone was shorter than in carbonate. Regardless of the thickness of the cement sheath, the highest strains were located at the casing-cement interface in carbonates. As a result of the temperature and pressure ramp, the cement sheath in sandstone failed by generating tensile radial cracks along the lowest layer thickness of the cement sheath. In compliant formations such as sandstone, the cement sheath would likely fail due to tensile cracking along its lowest thickness.