This paper presents the results of an experimental study about the variation of the small strain stiffness under K0 conditions which means that the lateral deformations are restricted, for two lateritic soils with different weathering intensities. The specimens followed loading and unloading K0 stress paths in an oedometer apparatus equipped with piezoceramic transducers capable to generate and receive shear (S) and compression (P) waves simultaneously. The influence of the loading process on the elastic small strain modulus (E0 and G0) was studied. The compressibility curve of the soils was established for different structural soil conditions (natural, unstructured, compacted, and saturated). For the samples at natural conditions (i.e., undisturbed), the more weathered soil exhibits a greater stiffness than the underlying Horizon; however, when removing the structure by reshaping, the stiffness of the upper Horizon decreases below of the lower Horizon. The addition of water softens cementation and the effect of suction. The results confirm that weathering provides a structure that increases the stiffness of soils.