The Wide Wheel is a recent abrasion test method (WA) proposed for building stones. The WA test is carried out by special equipment using abrasive dust on prismatic building stone samples. The purpose of this study is providing a methodology for practical estimation of the WA values from dry unit weight (γ), open porosity (PO), P-wave velocity (VP) and uniaxial compressive strength (UCS) values. In the study, test data from previous studies were compiled. Multivariate regression analyses (MLR), Feed Forward Back Propagated (FFBP) and Generalized Regression Neural Networks (GRNN) algorithms of Artificial Neural Networks (ANNs) were employed in the analyses. Equations by MLR analyses to estimate the WA values for 5 models were proposed. Then, FFBP and GRNN analyses were performed, and their prediction performance results were assessed. All five models were determined to be strong enough to be used in practice, although FFBP and GRNN are found to be stronger in prediction capability than the MLR method. •The practical estimation of the abrasion resistance of building stones is an important issue in the selection of natural stones with suitable properties as well as being economical.•The Wide Wheel abrasion values of building stones can be estimated from basic properties as unit weight, open porosity, P-wave velocity, and uniaxial compressive strength.•Equations to estimate abrasion values of building stones were proposed by multivariate regression analyses.•Abrasion values of building stones were successfully modeled by Feed Forward Back Propagated and Generalized Regression algorithms of Artificial Neural Networks method which is commonly used soft computing technique in various fields of science and engineering.