Refractory materials are subjected to significant chemical and mechanical loads, leading to their degradation and shortened lifespan. Erosion, driven by shearing forces originating from melt flow, stands as a primary mechanism for refractory wear. Despite its critical importance, a consensus on methods for quantifying refractory erosion is lacking. This study applies an inverse calculation method to investigate the erosion resistance of alumina coarse grain refractories in slags within the CaO-Al2O3-SiO2 (CAS) and CaO-Al2O3-SiO2-MgO (CASM) systems at temperatures of 1450 and 1500 °C. The method combines computational fluid dynamics (CFD) simulations with typical finger-test experiments. The CFD model resolves the slag-flow domain for which the refractory represents a dynamic boundary whose movement is governed by an erosion rate obtained based on an analogy to the field of soil erosion. An inverse calculation routine is utilized in the iterative solving of the non-linear least-square problem of parameter identification. The results demonstrate reasonable sensitivity of the calculated erosion parameters to slag composition and temperature. Higher values of detachment rate are obtained for slags in the CASM system due to the larger slag basicity. These values increase with increasing temperature. Correspondingly, the values of the critical shear stress are lower for the experiments with CASM slags and these decrease with increasing temperature.