Common methods to simulate fracture propagation include e.g. the insertion of cohesive elements in the mesh at the expected fracture area or a regularization with a phase-field method [1]. The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith’s criteria Gc. The former method yields a strong mesh dependence of the fracture path due to the user-defined position of the inserted cohesive elements. The latter requires a length-scale parameter that smooths the sharp discontinuity, which influences the diffuse band and also results in mesh-sensitive fracture propagation results. Recently, a novel approach based on the optimization on Riemannian shape spaces has been proposed in [2], where the crack path is realized by techniques from shape optimization. This approach requires the shape derivative, which is derived in a continuous sense and used for a gradient-based algorithm to minimize the energy of the system. Due to the continuous derivation of the shape derivative, this approach yields mesh-independent results. In this talk, the novel approach based on shape optimization is presented, followed by an assessment of the predicted crack path using numerical calculations from a phase-field model. [1] C. Miehe, M. Hofacker, and F. Welschinger. A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199(45):2765–2778, 2010. [2] T. Suchan, K. Welker, and W. Wollner. A new shape optimization approach for fracture propagation. Proceedings in Applied Mathematics and Mechanics, 2022. To appear, DOI: 10.1002/pamm.202200124.