The invention relates to a method to control the movements of a flight simulator involving linear and angular accelerations perceived at a pilot's seat and involving mathematical transformations of a lateral position y and a roll angle .phi. for said accelerations, wherein mathematical transformations are used with at least one of the following corrections: --Feed-forward of a specific force error due to the y-position wash-out into a roll angle transformation function; --Decomposition of specific force at pilot's position and addition of complementary filters to reproduce suitable side forces in the pilot's seat due to lateral accelerations; --Mathematical transformations linking a pilot's' position in an aircraft and flight simulator to a motion base centroid.