In this paper, the electric induction force due to a time-varying current is used to account for the longitudinal recoil force exerted on the rails of railgun accelerators. The analysis is based on the Lorentz force law. The paper shows that the induction force is longitudinal to the rails, and that its magnitude depends on the location, speed, and acceleration of the armature, and can be the strongest at the heads of the rails as observed in experiments.