The appearance of cracks in structures is a very important issue, moreover, it is a complex problem on the numerical level. These cracks should never be taken lightly. They can be the sign of serious disorders especially if they are structural cracks. The objective of this article is to study the effect of the crack existence in civil engineering structures: concrete and metallic structure in terms of frequencies and eigenmodes using the extended finite element method X-FEM and to compare the results obtained with the classical finite element method (Structure without crack).