Marble is a fragile and heterogeneous material whose properties vary depending on the nature and origin of the marble. Therefore, the marble machining process requires the skills and know-how of the stone cutter to manually configure the machining parameters for each piece of marble. This study addresses the enhancement of quality achieved by marble drilling processes in the industry. The objective of this work is to drill marble with high quality performance and avoid fracturing the material. This article focuses on the process of drilling white Carrara marble with an abrasive water jet. This unconventional tool significantly reduces unwanted damage resulting from the drilling process (fractures, spalling) compared to the conventional drilling process (rotating abrasive tools). The effect of waterjet cutting parameters, namely jet pressure, stand-off distance, nozzle traverse speed, abrasive flow rate, and hole diameter on drilling tolerances is studied. Five defects in the drilling process are modeled in this work: surface roughness, hole circularity, hole cylindricity, hole location error, and hole taper, using analysis of variance of linear regression models and an artificial neural network width high accuracy. These models could be of great interest to stone cutters to configure marble machining parameters and improve marble manufacturing quality.