In recent years, humanity became strongly dependent on the deep subsurface. It can be used as the energy source as well as the storage facility. At some stage, both listed applications require injection of fluid or gas into the subsurface porous media. Under certain conditions, it may provoke growth of hydraulic fractures. The appearance of fractures significantly changes properties of the permeable media which, in its turn, affects the operational performance of the subsurface reservoir. Apart from that, hydraulic fracturing may also cause a nuisance to the human environment in the form of earthquakes. Ability to predict growth of hydraulic fractures and their geometry becomes crucial. For this purposes, numerical models are extensively used. In this work, a fully coupled hydro-mechanical model for hydraulic fracturing of porous media was proposed. Based on this model, an explicit computational framework was developed in C++ programming language allowing efficient modeling of a single fracture propagating. Proposed algorithm consists of the Discrete Fracture Model for multi-phase flow and contact-enriched Finite Element Model for geomechanics. Irwin’s failure criterion from Linear Elastic Fracture Mechanics concepts was adapted. Stress Intensity Factors are evaluated employing displacement extrapolation technique. The proposed model was extensively tested in various set-ups including single- and multi-phase flow in isothermal and thermal conditions. Both straight and turning fractures were modeled. Effects of the mesh geometry, material properties, and stress field anisotropy were analyzed in a series of tests. Obtained results were validated with the semi-analytical solutions. Proposed numerical scheme demonstrated its applicability to a wide range of tasks and showed a great potential for its extension to a larger group of applications.