The invention relates to a method for managing a power-steering motor designed to supply a force to assist the movement of a steering rack, said steering rack being mounted such as to be movable between at least a first position (P1) and a second position (P2) in order to be able to change the steering angle of a steered wheel. Said method comprises: defining a virtual end-of-travel threshold (S1, S2) strictly comprised between the first position (P1) and the second position (P2); and if the rack is detected as having crossed said virtual end-of-travel threshold (S1, S2) in a predetermined crossing direction (F1, F2), simulating, by means of the power-steering motor, an end-of-travel stop by including in the assistance instruction a resistance instruction that simulates the effect of a mechanical stop, such as a spring-damper or a mass-spring-damper, preventing the actuator member from progressing beyond the virtual end-of-travel threshold (S1, S2).