The present invention relates to an apparatus for cooling a hot steel plate which is processed and constrained by constraining rolls and a method of arranging and setting spray nozzles enabling uniform cooling in a direction perpendicular to processing. In the apparatus and method of the invention, the spray nozzles are arranged so that a value of n power of the impact pressure of the cooling water on the cooling surface integrated in the processing direction between pairs of constraining rolls becomes within −20% of the highest value in the direction perpendicular to processing, where 0.05≦n≦0.2.