A system for the storage of electric energy with reduced thickness for a vehicle with electric propulsion; the storage system comprises: a support plane; and a plurality of chemical batteries, each of which comprises at least one electrochemical cell that rests on the support plane and has a flat parallelepiped shape with two mutually parallel, opposite larger bases; wherein in each chemical battery the electrochemical cell is arranged parallel to the support plane and rests with a lower larger base on the support plane; wherein each chemical battery comprises an own compression system which presses directly on a larger upper base of the electrochemical cell opposite to the larger lower base, keeps the electrochemical cell pressed against the support plane, and is independent from the compression systems of the other batteries; and wherein the compression system of each chemical battery comprises a pair of support elements arranged on opposite sides of the electrochemical cell and at least one strap which is pulled taut between the two support elements, so as to press against a larger upper base of the electrochemical cell and, therefore, keep the electrochemical cell pressed against the support plane; the storage system is characterized in that: wherein each support element presents, for each strap, a bar around which the strap is wound in a loop; and each support element has the shape of a parallelepiped with a triangular transverse section and presents a series of recesses, each defining a corresponding bar. a support plane; and a plurality of chemical batteries, each of which comprises at least one electrochemical cell that rests on the support plane and has a flat parallelepiped shape with two mutually parallel, opposite larger bases; wherein in each chemical battery the electrochemical cell is arranged parallel to the support plane and rests with a lower larger base on the support plane; wherein each chemical battery comprises an own compression system which presses directly on a larger upper base of the electrochemical cell opposite to the larger lower base, keeps the electrochemical cell pressed against the support plane, and is independent from the compression systems of the other batteries; and wherein the compression system of each chemical battery comprises a pair of support elements arranged on opposite sides of the electrochemical cell and at least one strap which is pulled taut between the two support elements, so as to press against a larger upper base of the electrochemical cell and, therefore, keep the electrochemical cell pressed against the support plane; the storage system is characterized in that: wherein each support element presents, for each strap, a bar around which the strap is wound in a loop; and each support element has the shape of a parallelepiped with a triangular transverse section and presents a series of recesses, each defining a corresponding bar. wherein each support element presents, for each strap, a bar around which the strap is wound in a loop; and each support element has the shape of a parallelepiped with a triangular transverse section and presents a series of recesses, each defining a corresponding bar.