In mountain tunnels, when the ground behavior is showing time-dependence characteristics, it would be extremely beneficial if future displacement could be predicted quickly and the results could be used to evaluate the effectiveness of countermeasures. In this paper, we proposed a structural Deteriorating type Voigt model (D-Voigt model), which incorporates into the Voigt model a mechanism in which the structure deteriorates with increasing strain. The three exact solutions derived from the constitutive equations of this model have the characteristic that the creep behavior can be expressed in three stages depending on the changes in external pressure. Therefore, in the acceleration stage, we verified the displacement reproduction of the D-Voigt model and prediction using the other models. And, a method for evaluating the internal pressure of countermeasure as a support effect was studied. Furthermore, the D-Voigt model was used to derive an effective prediction equation of countermeasure, and the relationship between the internal pressure caused by countermeasure and the effective prediction equation of countermeasure was clarified, and its validity was evaluated based on past cases.