Vertical displacement (VD) estimation is one of the most important topics in construction of an underground powerhouse cavern. This phenomenon commonly depends on excavation progress and corresponding geometrical, geological and geomechanical conditions of surrounding rock masses. Although many researchers investigated this issue, however, application of the new powerful predictive models is essential due to the topic complexities and limitations of previous methods. This study focuses on the estimation of VDs at the middle and key points on the roof and floor of a powerhouse cavern using the numerical analysis (NA), neural network (NN), fuzzy logic (FL) and statistical analysis (SA) models under various conditions. Rock geomechanical characteristics and geometrical variables of powerhouse related structures regarded as inputs in numerical analysis of VDs. On the basis of a large number of numerical simulations, a new predictive equation considering seven effective basic factors was fitted to predict the elastoplastic vertical displacement at the key points on roof and floor of powerhouse cavern. Through the numerical analysis, an enough datasets was introduced to construct and develop the NN, FL and SA models. Based on the testing datasets, the achieved results from these models were compared with each other as well as with the results of NA-based equation using the relevant statistical indices. This comparison confirmed that the performance of FL and NN models are relatively better than the NA-based equation. Moreover, these three models are more relevant than the SA model. At the end of modeling, conducted sensitivity analysis proved that overburden depth, lateral stress coefficient are the most effectual variables on the VDs whereas the tensile strength is the least ones.