Accurate reproduction of complex geological architectures is necessary to build realistic reservoir models, especially since these architectures are often important to flow behavior.Classical geostatistics presents severe modeling limitations because it only accounts for one-and two-point structural information. Complex geological structures cannot be captured based on these very restraining measures of spatial continuity (Caers, 2005). A particular heterogeneous architecture,significant to the oil industry, is carbonate buildups. The objective of this thesis is to “better”characterize common geo-structures and architectural elements that are often present in carbonate buildups. A typical example from the Sacramento Mountains in Southern New Mexico is analyzed, thenmodeled,using two main geostatistical algorithms: two-point statistics (TPS)-based SISIM, and multiple-point statistics (MPS)-based SNESIM. Both models are conditioned to facies pseudo-wells interpreted from high-resolution LIght Detecting And Ranging (LIDAR) images of outcrops, themselves located in three canyons that intersect the buildups.MPS-based algorithms extract structural information from conceptual 3D representations of reservoirs, called training images, that depict prior geological understanding. Algorithms are designed and coded to generate geologically realistic training images of carbonate buildups. Advanced MPS techniques, such as subgrid and multigrid simulations, targeted global proportions, and vertical proportion maps,are required to adequately model this complex carbonate stratigraphy. The MPS-based model is compared to a TPS-based model, representative of traditional geostatistical models, by quantifying their similarities to the training image (true reference) using statistical and heterogeneity measures. Assuming that visual, statistical and flow behavior similarity to the training image indicates a“better” model, we conclude that the MPS-based model, as compared to its TPS analog, is the “better” alternative for the particular algal buildup studied. Despite this result, this thesis does not suggest that MPS techniques are, in general, the “superior” alternative. On the contrary, based on the parallel modeling performed of both simple and complex architectural elements, we observe that the more “appropriate” stochastic technique is not only application-specific, but also goal-and data-driven.