Assume the material of concrete structure with crack is viscoelastic material, the relative displacement of crack side increases under load. If stress intensity factor is calculated by displacement direct method, the stress intensity factor will increase and may be even bigger than the concrete’s fracture toughness. The fracture problem of viscoelastic material is studied based on Entropy theory. It is showed that if the structure is viscoelastic material, there is no energy dissipation and release during the rheological process; the entropy is a constant and the crack remains stable, which means the displacement direct method is not feasible to rheological fracture problem. The blunt crack band model is preliminarily studied as well. It is believed that when fracture expanding element cracks, the structure energy will release, which is equal to the energy difference value between external work external work and total elastic energy and also approximately equal to the difference value between the total elastic energies of fracture expanding elements before and after cracking. As to linear elastic fracture problem, the stress intensity factor can be obtained by simply transforming the ratio of the energy difference value and virtual expanding length (plane problem) or virtual expanding area (spatial problem). It is also indicated by the analysis that blunt crack band model is independent of mesh size partly and its mesh can be obtained easier comparing with discrete crack model.