The generalized effective stress variable method for unsaturated soils was applied to the triple-shear strength criterion to obtain the generalized effective stress triple-shear strength criterion for unsaturated soils. Based on this criterion, the three-shear destructive stress ratio and the new yield surface equation under the generalized effective variable method were derived. Subsequently, by introducing the S-R decomposition theorem within the framework of finite deformation elastoplastic theory, a three-shear finite deformation elastoplastic constitutive model suitable for normally consolidated unsaturated cohesive soils was established. Comparison between the established constitutive model and the conventional triaxial test of unsaturated soil shows that the simulation results of the finite deformation constitutive model are in good agreement with the test points, which verifies the feasibility of this constitutive model for finite deformation elastoplastic analysis of geotechnical materials. Comparison between the established constitutive model and the infinitesimal strain constitutive model shows that the calculation results of the established constitutive model are more accurate than the calculation results of the infinitesimal strain constitutive model under the same conditions of initial compaction, net confining pressure and matrix suction. The numerical simulation results of the true triaxial consolidation and drainage test show that, all other conditions being equal, the deviatoric stress and volumetric deformation of the soil body is positively correlated with the influence coefficient of the intermediate principal stress.