This present study explored the Böhme abrasion value (BAV) of natural stones through artificial neural networks (ANNs). For this purpose, a detailed literature survey was conducted to collect quantitative data on the BAV of different natural stones from Turkey. As a result of the ANN analyses, several predictive models (M1–M13) were established by using the rock properties, such as the dry density (ρd), water absorption by weight (wa), Shore hardness value (SHV), pulse wave velocity (Vp), and uniaxial compressive strength (UCS) of rocks. The performance of the established predictive models was evaluated by using several statistical indicators, and the performance analyses indicated that four of the established models (M1, M5, M10, and M11) could be reliably used to estimate the BAV of natural stones. In addition, explicit mathematical formulations of the proposed ANN models were also introduced in this study to let users implement them more efficiently. In this context, the present study is believed to provide practical and straightforward information on the BAV of natural stones and can be declared a case study on how to model the BAV as a function of different rock properties.