Phase-field models are used to represent the geometry of defects in a diffuse manner, without introducing sharp discontinuities. Due to this feature, these models demonstrate a high level of efficiency in simulating crack propagation compared to numerical techniques that rely on a discrete crack model. This particular advantage becomes exceptionally evident when confronted with complex crack models, highlighting the superior capabilities of phase-field models to accurately represent the complex behaviors exhibited by cracks, and the phase field method can essentially be treated as a multi-field problem, even for a purely mechanical problem. The current study focuses on the area of ​​crack modeling in brittle materials, using the phase-field methodology specifically adapted to these materials. In the field of computational mechanics, many research efforts have focused on the complex task of fracture modeling through the use of phase fields. Among this body of academic work, the present study stands out for its use of a phase-field model to describe crack initiation and propagation in brittle two-dimensional materials using the finite element method (FEM). Numerical simulations are meticulously presented and carefully studied to vividly illustrate the remarkable efficiency and robust capability of the phase field method to address and handle this particular type of modeling.