In this work some geotechnical and soil-structure interaction problems are studied using the finite element method coupled with a Fourier transform technique. For linear elastic problems, Fourier transforms are applied to the governing field equations, thus enabling that some specific tridimensional problems can be analyzed using a 2D finite element mesh. In conventional finite element applications, a 3D discretization is usually required, but difficulties associated with the preparation of the finite element mesh and the involved computational efforts prevent, in general, the use of a true 3D model. The integral transform method is used in this research for the analysis of some very common problems in geotechnical engineering, such as piping systems, raft foundations and tunnels, where the geometry and the soil profile may be considered constant along a coordinate direction. The applied loading, however, can assume any possible surface distribution, which does not allow to treat the problem under the plane strain assumptions. Some special finite elements presented in the literature, called joint or interface elements, are also incorporated into the finite element computational program written in this research, given that for soil-structure interaction problems the material behavior at the common interface may greatly affect the entire system results. Some numerical examples are presented, and their numerical results are compared, whenever possible, with other solutions obtained using analytical or other numerical technique. Advantages and limitations of the integral transform method to solve tridimensional geomechanics problems are also discussed in this work.