Disc instability can play an important role in evolution of disc galaxies. In this talk, dynamical instability analysis for fragmentation of spiral arms is presented. Our previous work has demonstrated that our analysis based on linear perturbation theory can characterize well spiral-arm fragmentation and clump formation. In this study, our instability analysis is developed to take into account effects by toroidal magnetic fields. From the linear perturbation analysis for spiral arms, toroidal magnetic fields are generally expected to destabilize spiral arms. We, furthermore, test our linear analysis by adopting it to MHD simulations using isolated galaxy models.