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The issue of stochastic reconstruction of chalk samples containing appreciable amount of vuggy porosity in the form of foraminifer shells using a conditional simulated annealing (SA) technique is addressed. A new indicator function suitable for the algorithm is defined to represent chalk microstructures. Most of the chalk samples consist of vuggy porosity associated with large cavities found in foraminifer shell fragments or other dissolution features. These features have significant influence on fluid and electric transport properties depending on how they are interconnected and how much contribution they have to the overall porosity. Stochastic reconstructions using the widely used conditioning and truncation of Gaussian random fields method or the conventional SA technique are not adequate to reproduce them accurately. In conditional SA, the special features of interest are masked and are excluded during perturbation steps of the algorithm. We demonstrate the applicability of this technique in reconstructing foraminifer shells of different shapes and statistics in chalk samples using different combinations of the morphological descriptors.