Centrifugal force acting on a rotating disk induces in-plane loads in the radial and circumferential directions. An application of fiber-reinforced composite materials to a rotating disk can satisfy the demand for increasing its rotating speed. However, previous researches have been confined to single lamina disks. In this paper, a stress analysis of rotating disks made of multidirectional laminates is performed. The Tsai-Wu failure criterion is applied to the strength analysis of the rotating laminate disks, from which the maximum allowable speeds are obtained. The cross-ply ratios providing the maximum allowable speeds are obtained for the glass/epoxy and carbon/epoxy cross-ply laminate disks with CD geometry.