Nowadays erosion has several important applications in modern electrode surface treatment technologies. Experimental study of erosion processes [1] is a challenging task which promotes researches to develop numerical tools for quantitative analysis of this phenomenon [2].  We proposed 2D/3D approach to numerical simulation of thermal erosion caused by ion beams via finite-elements methods. State of eroding electrode is described in terms of heat transfer equation (1) written in energy form: where E - local enthalpy, T - local temperature, ρ, κ, C - density, thermal conductivity and specific heat respectively, h - distributed heat generation caused by ion beam. Last formula in (1) defines T as function of E because C(T) > 0. This dependence makes (1) closed-form and allows to take into account latent heat Λ of gas-solid phase transition.  Due to propagation of erosion front it is necessary to adjust heat source h during simulation:  where h₀ - initial configuration of heat generation, Δz - z-coordinate with a respect to erosion front z_f, E_crit - energy threshold for solid phase of electrode material, T_crit - phase transition temperature, θ - Heaviside function. To avoid heat transfer over erosion front it is assumed that κ = 0 if E ≥ E_crit.  We applied proposed approach to simulate erosion of small cylindrical CuCr-alloy electrode exposed to an argon ion beam. Fig.1 shows system geometry. Fig.2 shows computed relation of erosion coefficient and beam current density, each plot point corresponds to an identical erosion volume.