Storage system for storing crates comprising: a plurality of support elements (1, 30; 101; 111; 121; 131; 141) for storing crates, wherein the support elements (1, 30; 101; 111; 121; 131; 141) are elongate elements having a cross section that is substantially formed in an U-shape, comprising a continuous bottom section (13; 103; 113) and two opposite side walls (14; 104; 114) extending from the bottom section (13; 103; 113), wherein the side walls each comprise a top portion, forming two elongate supporting areas, whereby the elongate supporting areas are configured to support a crate or a column of stacked crates, wherein inner side sections of the side walls (14; 104; 114) each comprise a step protruding, preferably symmetrically, to the inside of the U-shape forming two elongate running surfaces, whereby the elongate running surfaces are configured to support a conveyor system for transporting the crate; wherein each of the plurality of support elements is monolithic, and wherein each of the plurality of support elements (1, 30; 101; 121; 131; 141) is formed of concrete or steel; wherein the storage system further comprises: a plurality of crates arranged on the top portions of the side walls (14; 104; 114; 124; 134; 144) of the support elements (1, 30; 101; 111; 121; 131; 141), wherein the crates have a substantially rectangular perimeter defined by upstanding front and rear walls and opposing side walls, wherein preferably the length of the crates between the front and rear walls substantially corresponds to the distance between the side walls (14; 104; 114; 124; 134; 144) of the support element (1; 101; 111; 121; 131; 141). the support elements (1, 30; 101; 111; 121; 131; 141) are elongate elements having a cross section that is substantially formed in an U-shape, comprising a continuous bottom section (13; 103; 113) and two opposite side walls (14; 104; 114) extending from the bottom section (13; 103; 113), wherein the side walls each comprise a top portion, forming two elongate supporting areas, whereby the elongate supporting areas are configured to support a crate or a column of stacked crates, wherein inner side sections of the side walls (14; 104; 114) each comprise a step protruding, preferably symmetrically, to the inside of the U-shape forming two elongate running surfaces, whereby the elongate running surfaces are configured to support a conveyor system for transporting the crate; wherein each of the plurality of support elements is monolithic, and wherein each of the plurality of support elements (1, 30; 101; 121; 131; 141) is formed of concrete or steel; wherein the storage system further comprises: a plurality of crates arranged on the top portions of the side walls (14; 104; 114; 124; 134; 144) of the support elements (1, 30; 101; 111; 121; 131; 141), wherein the crates have a substantially rectangular perimeter defined by upstanding front and rear walls and opposing side walls, wherein preferably the length of the crates between the front and rear walls substantially corresponds to the distance between the side walls (14; 104; 114; 124; 134; 144) of the support element (1; 101; 111; 121; 131; 141). a plurality of crates arranged on the top portions of the side walls (14; 104; 114; 124; 134; 144) of the support elements (1, 30; 101; 111; 121; 131; 141), wherein the crates have a substantially rectangular perimeter defined by upstanding front and rear walls and opposing side walls, wherein preferably the length of the crates between the front and rear walls substantially corresponds to the distance between the side walls (14; 104; 114; 124; 134; 144) of the support element (1; 101; 111; 121; 131; 141).