The present research started from the need of dating back the rock engravings in the Apuane Alps mountain chain (north-west Tuscany, Italy) which are on horizontal marble surfaces and are characterized by the figures of billhooks (Italian “pennato”) traced in contour line and whose chronology and meanings are still unknown.

For this purpose, in this paper we present a computer-aided mathematical study of the effects of natural erosion processes on an ancient linear trace engraved on a flat horizontal marble surface. The main goal is to demonstrate that the engravings are still visible after a long time exposure to natural erosion.

The mathematical technique used is the so-called Montecarlo method which consists of the study of the macroscopic properties of a granular system starting from the continuous repetition of microscopic stochastic events whose probability laws is supposed to be known. These laws were related to the erosion speeds of the two main erosion mechanisms for limestone, such as the freeze-thaw and the chemical dissolution, this last depending on the average annual rain fall.

By using the above described procedure, it was possible to observe the time evolution of the cross-section of the engravings in a time range spanning about 2000 years and to evaluate the trend behaviours of both depth and width of the small moat. From the analysis of these trends and from an estimation of the average annual rain fall, an algorithm was obtained to calculate absolute dating of the engravings.

In the last part of the paper, the results of the first experimental application of the present method on the so-called “Billhook Step” (Mount Gabberi, Apuane Alps) are exposed and discussed, also in terms of the influence of both random and systematic errors.