Although uniaxial consolidation of sediments in basins defines one of the most common and simple of geologic stress paths, there is remarkably little information concerning lateral stresses and elastic moduli associated with this process. Short-term relationships explored by geotechnical engineers show that ratios of effective horizontal stress (&sgr;h') to effective vertical stress (&sgr;&ngr;') or KQ, are constant for a given sediment over the low-stress range, but there is no consensus as to whether these ratios remain constant at the higher stresses and longer durations of geologic conditions. A series of uniaxial consolidation tests on a silty clay and a fine sand, including several elastic unload-reload cycles, were carried out to explore consolidation and elastic relationships to a &sgr;&ngr;' of 35 MPa. Over this stress range, KO remained constant for the clay (0.62) but increased slightly for the sand (0.44 to 0.53). The unload-reload cycles showed that the vertical Young's modulus (E&ngr;) increases markedly with consolidation stress (&sgr;c'). These cycles also demonstrated that &sgr;j'/&sgr;&ngr;' (elastic) is greater for clay (0.35) than for sand (0.21), but this ratio shows no variation with &sgr;c'. This implies that Poisson's ratios (&ngr;) did not vary significantly with &sgr;&ngr;' or &sgr;c' over the stress range of the tests. Comparisons with natural sediments suggests that cementation results in increases of E of up to an order of magnitude above that of an analogous uncemented sediment, but does not seem to affect &ngr;. The effect of geologic time on KO was explored using results of sparse applicable in situ stress measurements; these suggest not only that clay-rich sediments can support significant differential stresses, but also that stress ratios may even retain their short-term values for 106 yr or more. ¿ American Geophysical Union 1992