The aviation fabric reinforced rubber seal structure is the key component of aircraft cabin seal and load transfer mechanism, and its performance directly determines the safety and reliability of high-performance aircraft. The inner and surface fabric rubber layers of the cladding are characterized by a macroscopic nonorthogonal anisotropic constitutive model and a representative volume element based on mesostructure, respectively. Compared with the conventional single/ring belt seal, this novel cladding/core type of seal involves the strong anisotropy; the pretightened assembly process; and the interaction of cladding/core, cladding/fixture, and core/fixture. The effectiveness of the macro- and mesoscopic analysis method is verified by experiments and numerical simulation. In addition, the effects of friction coefficients, pretightened displacement, and material orientations on the mechanical behaviors of the seal are also investigated. To our knowledge, this is the first systematic study on the cladding/core type of seal structures, and our results provide a valuable reference for the evaluation and optimization of aircraft seal in henceforth research.