The article is devoted to mathematical and physical modeling of the process of hydraulic fracture initiation and propagation in the material with known physical-mechanical properties. Fracture toughness was the main focus of the research as it is a parameter characterizing the rock's ability to resist fracturing process. This parameter alongside with rock elastic properties and pumping conditions is one of the governing parameters while considering the fracture propagation in terms of mechanics of brittle fracture. The study is aimed at understanding the impact of fracture toughness on geometric properties of a fracture by means of numerical modeling of laboratory experiments of hydraulic fracture propagation in a model material. The strength properties including fracture toughness of the used model material have been studied using the indentation methods. The difference between experimentally observed and numerically calculated (keeping in mind the estimated strength properties) fracture geometry is studied in the paper and the possible reasons for this difference are discussed.