Abstract: Crack propagation in solid materials has always been one of the most common failures in engineering. The unified phase field theory has certain advantages in simulating crack propagation, but the traditional finite element method has great difficulties in discretizing the complex region of the phase field. Therefore, we combine the polygonal finite element method with the unified phase field damage model for the first time, and develop a polygonal finite element unified phase field damage model based on Matlab software. This model adopts the polygon discrete method and solves it by the sub-problem interleaved iterative algorithm, that is, the displacement field is solved by the fixed phase field, and then the phase field is solved based on the displacement field results, and the cycle calculation is repeated until the two results converge. By comparing the crack propagation results of L-shaped plates under the discrete quadrilateral elements and polygon elements, it is found that the calculated results of the polygon phase field are basically consistent with the traditional finite element calculations and experimental results, which proves the reliability of the method. The polygon finite element method of unified phase field theory is expected to play an important role in the discretization of complex areas of engineering structures.