Abstarct: Predicting the mineral grade at unobserved locations and determining prediction errors, particularly when conventional statistical methods are inadequate due to various reasons such as limited observations, high standard deviation, complex tectonic and geological variations, and skewed data distributions, are critical issues in mining exploration. In geostatistical studies, predictions are typically made under the assumption of a Gaussian random field, but, this is often not the case in practice. In such scenarios, a model-baxsed geostatistical approach is recommended. This thesis addresses the challenges and difficulties of these predictions and employs a Bayesian approach for two-dimensional and three-dimensional modeling of real mineral data. Given the density of geostatistical data and the complexity of posterior distributions, which lack closed-form solutions, the integrated nested Laplace approximation (INLA) is used to ensure rapid computations. The spatial model defined over the mining area is transformed into a Gaussian Markov random field (GMRF) using triangulation and the stochastic partial differential equation (SPDE) approach. Finally, the results of this method are compared with those of kriging. The implementation of the combined INLA+SPDE method on a three-dimensional geostatistical dataset represents a novel approach capable of overcoming these challenges. This is a new contribution to the field of mineral data modeling, evaluated in this thesis using several real-world mining examples, demonstrating its applications in geosciences.