This work focuses on simulation of dissolution and erosion of refractory materials by melts and on calculation of wear parameters. The experimental basis is given by the finger-test experiment for which a state-of-the-art device is used. Laser scanning of the worn surface of the sample after the experimental steps provides the erosion/corrosion profiles used for model validation and inverse calculation of wear parameters. Computational fluid dynamics is employed for resolution of the flow-field induced by the rotation of the sample in the melt. The dissolution model represents an improvement to the literature because it includes the effect of the Stefan velocity in the species boundary layer thickness and the convective part of the dissolution mass flux. Moreover, an asymptotic boundary layer approach for large Schmidt numbers is employed for reducing the computational needs in the model. The model was successfully verified against documented mass transfer equations and validation was obtained by comparison with the finger-test experiments. The determination of effective binary diffusivity was conducted by two methods: from the experimental average mass flux density and by curve fitting of the simulated dissolution curves to the experimental one. The results agreed with results presented in the literature and to those derived independently by confocal laser microscopical investigations. The model for refractory erosion accounts for the change of the sample geometry with time and the simulation output is a simulated erosion profile. The erosion law was a function of the wall shear stress and was based on an analogy between refractories and soils. An inverse calculation procedure for determination of the erosion parameters was programmed and tested firstly with artificially generated erosion profiles. The test-problem revealed the feasibility of inverse calculation with a two-parameter erosion law. Later, the inverse problem was successfully applied for inverse calculation of the erosion parameters in the erosion of an alumina coarse grain refractory sample.