Modeling wave propagation around very long structures such as bridges or tunnels is a major issue in the fields of either earthquake engineering or ground borne vibrations induced by car or railway traffic. Indeed despite a seemingly bidimensional or periodic geometry, a true three-dimensional analysis has to be carried out since the loads are fully three-dimensional. Unfortunately usual 3D models are not able to account for such large structures either from the theoretical or the numerical point of view. The development of a periodic approach able to account for 3D loadings is addressed in the paper. Moreover, for such large geometries an accurate knowledge of either the loads or the soil parameters cannot be usually achieved. Consequently the analysis is also carried out in a stochastic sense using the deterministic tools previously defined. The cases of random moving loads and random incident field is studied in detail.