First article on crack propagation was published by A. A. Griffith in 1921, in which crack was believed to propagate on condition that the variation of potential energy held in an elastic body was equal or greater than the surface energy due to a corresponding small crack growth. Later on, from 1950's, people started to realize that the plastic deformation and damage or dislocation of solid crystals also played an important role and should be taken into concern when evaluating cracking. These theories assume that fracture is essentially manipulated by the crack tip near-field characteristics. More recent studies revealed that fracture is better described by combining thermodynamic factors within a region called "fracture process zone (FPZ)" in which the correlation of energy consumption rate and fracture resistance plays a dominant role.

Dynamic crack propagation theory arose from studies of crash and explosion related problems. Simplified dynamic propagation models of single crack and multiple cracks with equal length can be found in the literatures. However, in fact non of the currently available major commercial codes are able to manage such problems. Among all the difficulties that encountered when it comes to numerically solving the problems, re-meshing scheme is the first challenge for FEA and such moving boundary conditions have not yet been untangled properly. Some viable tools are developed with other numerical approaches such as weighting function method (a semi-analytical solution), boundary element method, and Element Free Garlerkin method, etc.

People tend to believe that fracture criteria are different for various materials. Surface energy based Griffith rule has been successfully applied to predict cracking of many steels and alloy steels, while the FPZ approach is more appropriate for quasi-brittle materials, such as rocks and ceramics.

Among others, following points are sometimes considered when performing an FEA analysis: