It has been revealed from the long term consolidation test that the e-logp relation is linearly shifted with decrease in the strain rate in logarithm scale. The minimum strain rate measured by the conventional long term consolidation test is at most in the order of 10-9s-1. Question arises whether such a shift of the e-logp relation continues at even the infinite small strain rate, for example, smaller than 10-9s-1. To investigate the strain rate dependency of cohesive soil, the relaxation test was carried out for Osaka Pleistocene clays. It may be considered that in relaxation test, recoverable strain decreases due to decrease in acting pressure, and the irrecoverable strain equally increases, because the total strain remains constant. In this paper, assuming that the isotaches model can be applied to the irrecoverable strain, the strain rate dependency at very small strain rate was obtained from a series of relaxation tests. In this investigation the “strain rate dependency ratio” (SRDR) is defined as the ratio of the stress in the same e or e under the objective strain rate, based on the strain rate of 3.3×10-6s-1. It is revealed that the SRDR at infinite small strain rate is about 0.7.