This work deals with the nondestructive testing of foundations by means of a seismic imaging procedure. Our goal is to propose an inversion scheme that determines the shape of the foundations from the measured data with an acceptable computational effort. The inversion procedure was defined from a model based on the linear elastic wave equations in two dimensions. The inverse problem is particularly difficult to solve for several reasons: the distribution of numerous physical characteristics must be estimated, the relation between the underground characteristics and the measured data is highly nonlinear, and this is a large scale and ill conditioned problem. Three inversion techniques are proposed. They minimize a regularized least-square criterion iteratively. The first circumvent the difficulties of the problem by means of algorithmical and mathematical techniques. It favours the reconstruction of smooth areas separated by sharp boundaries. Two additional methods were developed. They take into account more specific characteristics of the problem. Tests were performed on synthetic data. The results show that the first method leads to satisfying results. The addition of more specific priors leads to more precise and faster reconstructions.