A strong relationship between the shapes of glacier excavation and some specific structures of the bedrock seems to exist in all the cases observed by the authors. Important examples of this kind include present and Quaternary glaciers in the Iberian Peninsula, the Alps, and the Peruvian Andes. A preliminary mathematical model has been developed, a brief description of which is given in this paper. Within the framework of this model the above interdependence can be interpreted. In this way the excavation mechanism that occurs in stationary glaciers can be explained without requiring the use of more sophisticated theories implying quite complex morphological phenomena. Suggestions for further studies are also made.