Abstarct: The use of mechanical rock properties to study underground spaces is called geo-mechanic. Geo-mechanic is one of the most important branches of science in exploring and drilling underground reservoirs, especially oil reservoirs. Most of the data obtained in geo-mechanical studies are geostatistical data. Modeling and analysis of such data require spatial statistics methods. However, much of the geostatistical data in geo-mechanical studies are three-dimensional, making it challenging to develop spatial statistical models and efficient computational methods for their analysis. In this thesis, we propose two new methods for analyzing three-dimensional spatial random fields, for the first time, to address the mentioned challenges. First, we introduce a nonparametric method called three-dimensional median polish to estimate the trend function of a spatial random field. Employing this method, we also develop a median polish kriging method. We also compare the proposed median polish kriging's performance with universal kriging, in which the trend function is estimated using the spline method. The performance is assessed using both simulated and real examples of uniaxial compressive unconfined compressive strength in one of Iran's oil reservoirs. Second, using a Bayesian approach, called Integrated Nested Laplace Approximation (INLA), and its combination with Stochastic Partial Differential Equations (SPDE) method, we will develop the analysis of three-dimensional continuous indexed spatial random fields.