Numerical study on crack propagation are of great importance for structure design and assessment. In this contribution, the floating node method (FNM) is combined with the symplectic analytical singular element (SASE) to form a new crack-tip element. The four node quadrilateral crack-tip element contains a SASE for the crack tip area to account for the singularity issue. Floating nodes are used to form a smooth transition mesh to full fill the other area of the element automatically once the SASE has been generated. Delaunay triangulation is used to guarantee the quality of the transition elements. Strong discontinuity resulted from complex crack networks with multiple cracks is treated by the FNM. Criteria for crack nucleation, propagation angle and length of new crack segment are given. Interaction between cracks and between crack and defect can be readily modelled without any prior knowledge of crack path. The fracture process of crack propagation can be modelled without remeshing. Inherited from the FNM, the proposed crack-tip element is especially suitable to be implemented in the form of a user defined element. Completed fracture processes with crack nucleation, propagation and interaction are modelled in the numerical examples.