The often striking presence of cyclical beddings has frequently been noted in Cretaceous marine sediment deposits. In many instances, these beddings appear to have periodicities similar to those of the Earth's orbit, i.e., its precession, obliquity, and eccentricity. Variations in the primary deposition of ocean sediments are strongly linked to atmosphere‐land‐ocean interactions. We report a set of numerical experiments using an atmospheric general circulation model that are designed to examine the sensitivity of mid‐Cretaceous climate to insolation changes due to the precessional cycle. We restrict attention to a single orbital parameter because most limestone/black shale bedded sequences were deposited at low latitudes, where precessional insolation variations predominate. We varied systematically the precessional index between the maximum positive and negative values calculated over the last 2 m.y. and used mid‐Cretaceous paleogeographic and paleotopographic reconstructions and zonally symmetric sea surface temperatures based on earlier work by Barron and Washington. Surface wetness and albedo values appropriate for grassland were prescribed uniformly over all land regions. To capture the seasonality of precession, we employed both perpetual January and perpetual July simulations. Changes in surface heating due to the imposed insolation anomalies resulted in a strong, basically linear response of monsoonal circulations, dominated by changes over the northern hemisphere. The hydrologic cycle shows a significant response over many regions. The low‐latitude proto‐South Atlantic region varies from a strong net sink for water vapor (excess precipitation) to a strong source (excess evaporation) over the precession cycle. This variation is consistent with an alternation between a stagnant, stratified ocean basin with anoxic bottom water and an evaporative basin that produces bottom water that is warm, saline, and oxygenated. The portion of the Tethys Ocean that overlays the limestone/black shale sequences now found in present‐day Italy does not exhibit comparable behavior, but the reconstruction of orography and basin boundaries in this region is less known. The simulations show, however, that as the monsoonal flow over south proto‐Asia intensifies, water vapor evaporated in this part of Tethys is prevented from crossing the proto‐Alps into the interior of the continent, thereby remaining in the Tethian drainage basin. As a result, central proto‐Asia shifts between arid and moist conditions with precessional variations. The water vapor budget over northeast Africa varies systematically from zero seasonality to a marked wet/dry seasonal cycle. The deposition of eolian material can be inferred from a combination of continental aridity, favorable mean wind directions, and significant wind variances. In our experiments the mean surface and upper winds often show a systematic response to precession, but surface wind variances show a systematic response only in isolated regions. Our simulations do not provide a simple mechanism to explain the cyclicity in eolian deposition that has been reported for north‐central Tethys.