A vertical lift storage system for inserting and withdrawing load units into and from a storage rack, comprising: a storage rack configured to store load units; a lift system with an upwardly and downwardly movable carrier structure, wherein the carrier structure is configured with a carrier floor for carrying multiple load units at respective multiple sections thereof and with first transportation means configured to insert and withdraw respective load units into and from the storage rack; wherein the carrier structure is configured with second transportation means for shifting load units sideways across the carrier floor, between its sections; the second transportation means comprises one or more rollers disposed between two neighbouring first transportation means; wherein the first transportation means are elongated and arranged parallel to the rollers to accommodate movement to insert and withdraw respective load units into and from the storage rack in a transverse direction; the first transportation means are configured with: - a support face; - a telescopic arm configured to move the support face in and out in the transverse direction, characterized in that it comprises: - means to lower and raise the support face relative to the carrier structure; wherein the first transportation means are configured as a lifting type which is lowered slightly below a load unit to leave the load while it slides below or is slightly raised to lift a load unit and thereby to insert or withdraw a load unit; wherein the first transportation means are configured with drive means for raising and lowering load units on respective sections in synchronism relative to the carrier floor; and wherein the first transportation means are configured with multiple drive means for inserting and withdrawing load units from/to respective sections individually from one another and for inserting and withdrawing load units from/to respective sections in synchronism. a storage rack configured to store load units; a lift system with an upwardly and downwardly movable carrier structure, wherein the carrier structure is configured with a carrier floor for carrying multiple load units at respective multiple sections thereof and with first transportation means configured to insert and withdraw respective load units into and from the storage rack; wherein the carrier structure is configured with second transportation means for shifting load units sideways across the carrier floor, between its sections; the second transportation means comprises one or more rollers disposed between two neighbouring first transportation means; wherein the first transportation means are elongated and arranged parallel to the rollers to accommodate movement to insert and withdraw respective load units into and from the storage rack in a transverse direction; the first transportation means are configured with: - a support face; - a telescopic arm configured to move the support face in and out in the transverse direction, characterized in that it comprises: - means to lower and raise the support face relative to the carrier structure; the second transportation means comprises one or more rollers disposed between two neighbouring first transportation means; wherein the first transportation means are elongated and arranged parallel to the rollers to accommodate movement to insert and withdraw respective load units into and from the storage rack in a transverse direction; the first transportation means are configured with: - a support face; - a telescopic arm configured to move the support face in and out in the transverse direction, characterized in that it comprises: - means to lower and raise the support face relative to the carrier structure; - a support face; - a telescopic arm configured to move the support face in and out in the transverse direction, characterized in that it comprises: - means to lower and raise the support face relative to the carrier structure; - means to lower and raise the support face relative to the carrier structure; wherein the first transportation means are configured as a lifting type which is lowered slightly below a load unit to leave the load while it slides below or is slightly raised to lift a load unit and thereby to insert or withdraw a load unit; wherein the first transportation means are configured with drive means for raising and lowering load units on respective sections in synchronism relative to the carrier floor; and wherein the first transportation means are configured with multiple drive means for inserting and withdrawing load units from/to respective sections individually from one another and for inserting and withdrawing load units from/to respective sections in synchronism.