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This paper presents the effect of different elastic acoustic and inelastic optical electron-phonon interaction mechanisms on quantum transport and electrical characteristics of multigate silicon nanowire FETs. A 3-D quantum-mechanical device simulator based on the nonequilibrium Green's function formalism in the uncoupled mode space that can handle electron-phonon interactions has been developed to extract the physical parameters of the devices. The electron-phonon scattering has been treated by using the self-consistent Born approximation and deformation potential theory. Utilizing this simulator, we show that interaction of the carriers with optical phonons redistributes the energy and momentum of electrons in the transport direction, depending on the energy of the phonon. Optical phonons cause either a reduction of the electron density or an increase of the electron concentration in the channel region, depending on the phonon energy and coupling strength. Finally, we show that the critical length for carriers to get backscattered in the silicon nanowire is directly proportional to the phonon energy.