Abstract. In this work, an advanced numerical model, based on the cohesive zone approach and the moving mesh technique, is proposed to simulate fracture propagation in quasi-brittle materials. In particular, the proposed numerical procedure consists of two stages. In the former one, according to the inter-element crack approach, once a suitable stress criterion for fracture onset is satisfied, a mesh boundary, representing the crack segment, is selected and aligned along the crack propagation direction by using the well-known moving mesh technique. In the latter one a zero-thickness interface cohesive element, equipped with a traction-separation law, is inserted on-the-fly along the previously selected mesh boundary, in order to describe the nonlinear fracture process. Comparisons with available experimental and numerical results have highlighted the effectiveness and the reliability of the proposed model in the prediction of the brittle fracture phenomenon.