Europa is one of the most interesting celestial world that has been ever observed. The habitability condition, met for the liquid water layer covering the moon, yields to astonishing speculations concerning what might exist in the interior of the tiniest moon of Jupiter. The Voyager and Galileo programs detected a frozen and brittle layer, deeply battered by lineament features. The observed crevasses on the moon's icy surface can be considered as results of a strong and variating stress field applied to the brittle icy shell that eventually reaches critical deformation conditions locally, and favors the process of crevasse propagation. The superimposition of secular widening to diurnal components is the source of stress that continuously deforms the brittle surface of Europa and induces the ice to crack, similarly to the processes observed with crevasses in large terrestrial ice sheets. The research's aim is to improve the existing models of fracture propagation for the Europa ice shell, dealing with analogs observed in Earth's crevasses on large ice shelves, by the implementation and the usage of linear elastic fracture mechanics (LEFM). Two different LEFM approaches are included in the document, one dealing with the estimation of global areas on the moon that are more favorable to host propagation and one dealing with the estimation of fractures' lengths for specific observed features. Results describe the existence of critical and non-critical areas centered in the equatorial zone which are respectively prone or not to host vertical propagation. Maximum critical depths for surface crevasses reach values of 120 meters, while critical heights for bottom crevasses show values up to 1.5 kilometers. Beside the outcomes of the vertical simulation, a mathematical manipulation of the LEFM analysis allowed the determination of horizontal cracks’ growth. Knowing the aspect of an observed lineament, the current model could calculate fracturing events’ intensity. These reach propagation rates of kilometers per second, namely almost instantaneous episodes. The outcomes of the current research are particularly interesting when seen in relation with the future exploration missions to Europa: ESA's JUICE, NASA Europa Clipper and its potential lander. Specific areas that are more prone to host propagation and the determination of growth rates are helpful elements in the preliminary description of target landing areas and the fracturing events’ detection possibility. The built model yields to a further and more accurate understanding of the dynamics for the interior of one of the most promising celestial object, in term of searching for a biosphere, hence extraterrestrial life.