The aim of this paper is the analysis of propagation of cohesive cracks through the formulation of hybrid equilibrium elements (HEE) with the aid of a minimal re-meshing algorithm, based on the rotation of the element sides, according to the direction of maximum principal stress at the crack tip. The HEE is an accurate stress-based formulation developed in the variational framework of the minimum complementary energy principle and it is an effective tool for inter-element fracture propagation analysis. The inter-element cohesive crack is modelled as an extrinsic interface embedded at every element side without any additional degree of freedom but, being in equilibrium with the element stress field, is modelled as a function of the same degrees of freedom of HEE, called generalized stresses. The direction normal to the maximum principal stress at the crack tip is assumed as the direction of crack propagation. The crack is meshed as an extrinsic interface embedded at the closest element side, which is rotated about the tip in order to be geometrically co-aligned to the crack. The HEE with the extrinsic interface embedded at the element sides has been implemented in an open-source finite element code, employing quadratic, cubic and quartic stress fields. Numerical simulations of some fracture propagation problems are presented and the related results discussed.