The contrast between the effective refractive indices (RIs) of the core mode in a uniaxial-crystal fiber yielded respectively by two fiber analysis models, namely the two-layered medium model and three-layered medium model, is simulated and analyzed. Based on this, the surrounding RI, temperature and axial strain sensitivities of a long-period fiber grating (LPFG) are calculated. The result shows that the core-mode effective RI difference produced by the two fiber analysis models is significant, especially in the case of thin cladding layer. Moreover, the surrounding RI, temperature and axial strain sensitivities calculated from the two layer model and/or the materials′ sensing-parameter-induced optical coefficients have significant error, and it is necessary to employ the three layer model and the correspondent model effective RI coefficients to obtain accurate results. The relationship between the sensitivities and the cladding mode order for different clad radii is calculated. This paper provides guidance to the analysis and design of LPFG based sensors.