Authors have proposed constitutive equations for rock based on the theory of non-linear visco-elasticity. The constitutive equations are grouped into two types: compliance or irrecoverable-strain monotonically increases with stress. In earlier studies, it was reported that both types of constitutive equations are applicable at least to the postfailure region. In this study, applicability of the constitutive equations to the pre-failure region was examined. At first, parameters were estimated from the results of unloading-reloading and alternating loading-rate tests under uniaxial compression. The calculated results with the estimated parameters were compared with the experimental results under various loading conditions. If a constitutive equation was properly selected, the equation well simulated the various time-dependent behaviors in the pre-failure region: loading-rate dependency of Young's modulus, creep and generalized relaxation where a set of parameter values was used in not only pre-failure but also post-failure region.