Rate effects on one-dimensional compressibility and undrained shear strength of a heavily overconsolidated naturally cemented clay have been studied. It is shown that in constant rate-of-strain consolidation tests the compressibility increases and the apparent preconsolidation pressure decreases with progressive decrease in rate of strain. Also a decrease in undrained strength is shown to occur with slower rates of strain in constant rate-of-strain shear and with increased time of sustained loading in creep tests. Undrained strengths from the two types of shear tests have been correlated.