In magnetic disk drives the slider carrying the read-write circuitry flies within a fraction of a micron from the storage disk over an air bearing during operation. When the unit is first started or turned off, however, the slider lacks the air bearing and slides in contact with the disk. In order to protect the disk as well as the slider from excessive wear, a thin layer of lubricant is applied to the surface of the disk during the manufacturing process. This lubricant, which exists in the form of a thin film of viscous liquid of a few hundred Angstroms thick, tends to drift outwards because of the rotation of the disk drive, which may spin at thousands of revolutions per minute. It is widely believed that surface roughness of magnetic storage disks plays an important role in retaining the lubricant layers on the disks. Descriptions of the surface asperities of the disks, however, are so complex that it would be necessary to draw upon statistical techniques for an adequate representation. The purpose of this investigation is to evaluate the effect of surface roughness on lubricant retention by methods of stochastic simulation. Surface roughness is treated as a random field with two characteristic length scales. It is found that surface roughness markedly enhances the retention of a thin liquid film on a rotating disk; the thinner the lubricant layer the dominant is the effect of surface roughness. Moreover, different topographic structures of the surface roughness lead to different asympotic limits of liquid retention.