Effective numerical methods for crack problems play a very important role in analysis of structure with crack. In this project, the well performed methodology of symplectic dual approach for applied mechanics is applied to the numerical analyze of dynamic and viscoelastic fracture mechanics. Firstly, adaptive expansion time-domain method is used to separate time coordinate variable, and the original problem can be transformed into a series of recursive-form boundary value problem. Then, a novel finite element with regular shape around the crack tips is selected, and the analytical singular finite element is constructed using the symplectic eigen-solution and special solution as interpolation functions. The stress and displacement fields around crack tips can both be described accurately in the singular element, and the corresponding fracture parameters can be specified directly, also the new numerical method can perform very well with satisfactory numerical stability when relative crack problems are considered. Meanwhile, the singular element is connected with outside regular elements directly without any transition element, and refined mesh around crack tips is also unnecessary. Numerical analyze of dynamic and viscoelastic crack problems in the structure with arbitrary shapes can be solved effectively, and the expected fracture parameters can be specified directly with highly solving accuracy.