Crack propagation is modeled via a phase field method with the consideration of the linear elastic behavior of metallic materials. A scalar order parameter is introduced to identify the intact phase and broken phase. A Ginzburg-Landau type free energy function is constructed to include the energy terms associated with elastic deformation, gradient of the order parameter and local energy contribution due to the order parameter. Evolution of the order parameter is modeled by the Allen-Cahn equation with a mobility parameter. The free energy function is then solved with the finite element method in accordance with the minimal energy principle. Two-dimensional examples of the mode I and II fracture problem are illustrated, and compared with analytical solutions.