We propose an accurate model for analyzing phase-shifted and cascaded long period fiber gratings (LPFG) as well as concatenated LPFGs having the characteristics of phase-shifted and cascaded LPFGs. To analyze the concatenated LPFGs with arbitrary wavelength spacing and line width, the coupling between the core mode and multiple cladding modes was considered. In order to obtain an analytical matrix model for the concatenated LPFGs, a multiport lattice filter structure was used. To verify the validity of the proposed model experimentally, we have fabricated two LPFG structures: cascaded LPFGs and concatenated LPFGs with three uniform LPFGs having the characteristics of cascaded LPFGs. We have observed that the transmission spectra calculated using our multiport lattice filter model are close to the corresponding measured spectra in the wavelength band of interest.