Underground rock engineering design continues to progress to complex and deep excavations in order to tackle increasing demand of minerals and metals. The responses of engineered systems in rocks, in general, are highly-nonlinear, time-dependent, uncertain, and not yet completely understood. The Finite Element Method(FEM), Discrete Element Method(DEM) and Boundary Element Method(BEM) numerical techniques have been widely applied in evaluating the design and stability of underground construction. In recent years, as machine learning (ML) algorithms have been implemented to predict the complex behaviors of rock engineered structures, engineers now can rely more on the ML-based data mining instead of carrying out a large number of numerical FE analyses particularly for a series of parametric studies. In this study we utilize the deep learning (DL) technique. This deep learning model is used to estimate the stress and the size and properties of the plastic zone for different arrangements and shapes of 3D openings. We start with simple shaped openings and simple in-situ stress conditions to consider the effects of excavation size, rock properties, and depth. In the future, we plan to progress towards more complicated shapes, in-situ stress conditions, and material properties. At first, the 3D numerical modeling and subsequent FE analysis is performed based upon the commercial finite element analysis program Abaqus. Next, user-defined python script along with Matlab are used to extract the output variables in the vicinity of the excavation boundaries, and the DL model is then designed and trained to take the simulation results and directly predict a set of output responses for a wide range of influence factors, bypassing the FEA computation. This study demonstrates the feasibility and great potential of using the DL techniques as a fast and robust alternative of FEA analysis in the geotechnical and mining industries, and is particularly well matched with the modern technologies for remote sensing and rock characterization.