To design underground structures and estimate their stability, it is essential to understand mechanical behaviors of rock and applicability of constitutive equations not only in compression but also in tension. In this study, the non-linear visco-elastic constitutive equations proposed by the authors in compression were applied to the behaviors in uniaxial tension. The deformation characteristics and mechanism in uniaxial compression and tension under dry and wet conditions were investigated by comparison of the mechanical properties and the constants in the equations. It was found that three non-linear visco-elastic constitutive equations can reproduce the stress-strain curves in uniaxial tension for Sanjome andesite in dry and wet, Kawazu tuff in dry and wet, and Inada granite in dry condition. Time-dependent behaviors of Sanjome andesite in dry condition such as loading-rate dependency and creep can be also reproduced with the same equations. Because the calculated results of unloading curves were not consistent with the testing ones, the new constitutive equation combining the previous ones was proposed. The testing results showed that strength degradation by water is larger in tension than in compression and that initial Young's modulus in tension is nearly equal to the slope of unloading curves in the pre-failure region in compression. Relationship of the constants in the constitutive equations under various testing conditions was discussed. The exponents representing the stress dependency of strain rate in transient creep were calculated with the constants in tension, and found to be consistent in the three constitutive equations under dry and wet conditions.