In this paper,a new plane shape-free multi-node singular hybrid stress-function(HS-F)element with drilling degrees of freedom,which can accurately capture the stress intensity factors at the crack tips,is developed.Then,a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently.Only simple remeshing with an unstructured mesh is needed for each simulation step.Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.