Monitoring data show that many landslides in the Three Gorges region, China, undergo step-like displacements in response to the managed, quasi-sinusoidal annual variations in reservoir level. This behavior is consistent with motion initiating when the reservoir water level falls below a critical level that is intrinsic to each landslide, with the subsequent displacement rate of the landslide being proportional to the water depth below that critical level. Most motion terminates when the water level rises back above the critical level, so the annual step size is the time integral of the instantaneous displacement rate. These responses are incorporated into a differential equation that is easily calibrated with monitoring data, allowing prediction of landslide movement from actual or anticipated reservoir level changes. Model successes include (1) initiation and termination of the annual sliding steps at the critical reservoir level, producing a series of steps; (2) prediction of variable step size, year to year; and (3) approximate prediction of the shape and size of each annual step. Annual rainfall correlates poorly with step size, probably because its effect on groundwater levels is dwarfed by the 30 m annual variations in the level of the Three Gorges Reservoir. Viscous landslide behavior is suggested.