The spectral response of long-period fiber gratings can be tailored by the cladding index perturbation (C-LPFGs) induced by written methods. Here, we investigate theoretically the effects of radial dependence and the magnitude of the cladding index modulation on the transmission spectra of C-LPFGs. Simple analytical expressions that describe the dispersion characteristics of the guided core mode and cladding modes are derived from a multilayer cylindrical waveguide. As the radial depth increases, we demonstrate that transition points exist for the resonances of lower cladding modes, i.e., LP06 and LP15 modes, by comparing the mode-coupling phase to the value π/2. In addition, we show that resonant wavelength shifts of all cladding modes follow the same trend. For the LPvj (v≠0) modes with two polarizations, the cross talk weakens the power exchanges between core mode LP01 and LPvj (v≠0) modes. Moreover, the coupling mechanism relating to cladding index modulation is explained by the presence of the interaction between the evanescent field of the core mode and cladding modes. This work is promising in terms of providing sufficient guidelines to understand and explore design and application of LPFGs.