Modern geodetic and seismic observations indicate that the majority of earthquakes result from unstable shear on quasi-planar faults. The thickness of the earthquake rupture zone is usually much smaller than its characteristic in-plane dimensions, which allows us to represent earthquake ruptures as shear cracks (Fialko 2007). Better understanding of shear crack development, propagation, and arrest can help us learn more about earthquake behavior and prediction. In earthquake fracture mechanics, both the inelastic yielding at the rupture fronts and the evolution of friction on the remainder of the slipping surface should be considered. Thus, crack models and friction models of an earthquake source should be intrinsically coupled and used jointly, but there is currently no theory that incorporates both effects simultaneously to describe earthquake rupture propagation. To develop such a theory, we study different friction and fracturing laws using Finite Element software PyLith and Abaqus. Mathematically, the crack growth in unbroken media and on pre-existing faults is very similar, provided that the slip surface is planar. That is why we consider planar ruptures in this work. We use Abaqus eXtended Finite Element Method (XFEM) to model brittle cracking and fracture propagation in an elastic material, and PyLith to model plastic yielding at the crack tip regions and apply different friction models along the fault. We test elastic and elastoplastic (i.e. Drucker Prager) materials with different parameters and different friction models on the slipping surface (i.e. static friction, dynamic friction, slip-weakening friction, rate-and-state friction). We monitor traction, slip, and slip rate distributions along the fault throughout the simulation to observe earthquake rupture propagation and parameter evolution depending on the characteristics of the system. In the rate-and-state friction simulations we observe instability generation on the unlocked fault section. Rupture propagation into the initially locked sections of the fault shows stress distributions near the rupture front similar to those for brittle cracking. These results provide more insight into the correlation between friction and fracturing theories for the case of earthquake ruptures.