We present an approach for simulation of topography related artefacts in local thermal conductivity measurements using Scanning Thermal Microscopy (SThM). Due to variations of the local probe-sample geometry while the SThM probe is scanning across the surface the probe-sample thermal resistance changes significantly which leads to distortions in the measured data. This effect causes large uncertainty in the local thermal conductivity measurements and belongs between most critical issues in the SThM when we want to make the technique quantitative. For a known probe and sample geometry the topography artefacts can be computed by solving the heat transfer in the SThM for different probe positions across the surface, which is however very slow and limited to single profiles only, if we use standard tools (like commercially available Finite Element Method solvers). Our approach is based on an assumption of diffusive heat transfer between the probe and the sample surface (and within them) and on the use of a Finite Difference solver that is optimized for the needs of a simulated SThM images computing. Using a graphics card we can achieve computation speed that is sufficient for a virtual SThM image generation on the order of few hours, which is already sufficient for practical use. We can therefore use the measured sample topography and convert it to a virtual SThM image which can be then e.g. compared to real measurement or used for artefacts compensation. The possibility of performing fast simulations of topography artefacts is also useful when uncertainties of the SThM measurements are evaluated. (C) 2017 The Authors. Published by Elsevier Ltd.