We model static fault friction - an important physical observation in rupture dynamics, using field dislocation mechanics (FDM). The energy density function in our model encodes accepted, simple physical facts related to rocks and granular materials under compression. We work within a 2-dimensional ansatz of FDM where the rupture front is allowed to move only in a horizontal fault layer sandwiched between elastic blocks. Elastic damage is allowed to occur only in the fault layer, characterized by the amount of plastic slip. The theory dictates the evolution equation of the plastic shear strain to be a Hamilton-Jacobi (H-J) equation, resulting in the representation of a propagating rupture front. A Central-Upwind scheme is used to solve the H-J equation. The rupture propagation is fully coupled to elastodynamics in the whole domain, and our simulations recover static friction laws as emergent features of our continuum model, without putting in by hand any discontinuous, ``off-on'' switching criterion. We fit a linear curve (which resembles the Mohr–Coulomb failure curve) to our simulation data and make a quantitative prediction of material constants for rocks like cohesion and friction angle. We demonstrate short-slip and slip-weakening dynamic responses depending on the amount of damage allowed behind the rupture front, and show supersonic and sonic rupture propagation in appropriate physical settings.