A rack for the storage of CD cases or other rectilinear objects preferably has a support providing two lateral wall components that hold or support the CD cases at least in the area of one of their diagonal ends by means of opposite, lateral contacts, whereby the lateral wall components that face the CD cases are arranged at an angle of greater than 90.degree. relative to each other, thereby forming an imaginary trapezoidal area. Cross supports are arranged between the lateral wall components for the purpose of forming compartments for the CD cases, said cross supports preferably being arranged as rod-shaped elements that are positioned with slight clearance within the vicinity of the diagonal lines of the CD cases, which are inserted diagonally between the lateral wall components in the direction of the apex of the angle.