Summary: Tension-compression asymmetry, thermal-mechanical coupling, and finite deformation effects are common characters of many biological materials and engineering structures. By introducing different elastic constants under tension and compression, a thermo-mechanical bi-modulus constitutive model and a subsequent efficient computational analysis framework are proposed in the finite deformation regime. After we validate the convergence, accuracy, and robustness of the algorithm, we investigate the mechanical behavior of human brain tissue under varying intracranial pressure and temperature. Furthermore, with the use of the proposed bi-modulus thermoelasticity model, the classic tension-field theory is regularized, and wrinkling region and its evolution in membranes under thermomechanical loads can be effectively predicted, as an alternative to the computationally intensive post-buckling analyses.