Several approaches can be taken to conduct seismic data inversion. However, usually, these approaches are unable to distinguish vertical and horizontal heterogeneities. Seismic inversion through the singular value decomposition (SVD) method offers an adequate and simple way to improve these traditional inversion models. For this study P and S wave data were acquired at a site located in northeastern Mexico, obtaining their travel times. An inversion algorithm involving the SVD analysis was then developed to establish the seismic velocities of the lithological units. Further, images of compressional and shear-wave velocities (Vp and Vs, respectively), Vp/Vs ratio, and elastic moduli (bulk, shear and Young's moduli, Lamé's constant, and Poisson's ratio) were obtained. These were compared with two geotechnical soundings positioned over a geophysical profile line. The geological features of the exposed units were recognized on some trenches. Further, seismic images demonstrated correlations with the thickness and distribution of the geological units. Unconsolidated sediments and fine-grain clastic rocks (in the Méndez formation) were clearly distinguished by the high velocity contrast. SVD seismic inversion has shown the ability to distinguish small physical heterogeneities of shallow geological units. Its application in civil engineering, hydrogeology, and to solve soil pollution problems can be relevant.