The system (1) has a storage and retrieval machine (10) assembled between an upper guiding rail (21) and a lower guide rail (22). The machine has a vertical mast (11) equipped with an upper guiding system (14). Stabilization units (18) comprise stabilization elements (181a, 181b) i.e. rotary rollers, cooperating with complementary stabilization elements (23a, 23b) of a storage system transversely displaced with respect to a median longitudinal displacement plane of the vertical mast in order to maintain a constant distance between the mast and the complementary stabilization elements.