Linear Elastic Fracture Mechanics (LEFM) are used to study crack propagation in unreinforced concrete of massive structures. This approach is well suited to the nonlinear analysis of structures of large dimensions, taking into account the size effect, i.e., the influence of the dimension of the structure on its behaviour at rupture. The Finite Element method is used to calculate the structure and the hypothesis of plane strain is made. The use of a criterion of crack propagation, based on LEFM requires the calculation of stress intensity factors. The evaluation of the latter is performed by the mean of a surface integral defined around the tip of the crack studied. It has been shown in this work that this integral is derived from the path integral J. The use of the surface integral has also been extended to the cases where body forces (gravity, inertie) act, or when the edges of the crack are subjected to pressure. This method is precise and numerically efficient. A smeared crack model is used in order to avoid continuous remeshing during crack propagation. But, as it has been shown in this research, classical smeared crack elements do not give satisfactory results when the crack is submitted to shear loading, a new finite element, using smeared cracking but with discontinuous shape functions has been developed. The model which combines LEFM and the smeared crack approach has been applied to different classical problems of fracture mechanics. It leads to good results under static or dynamic loading. As an example, the nonlinear behaviour of the vertical cross section of a gravity dam during an earthquake has been calculated and the crack pattern identified. Many further developments could be done starting from this original approach, in order to simulate more closely the real behaviour of structures, taking into account friction in the cracks and the three-dimensional development of then.