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To assess the hazards associated with the propagation of lava flows during volcanic eruptions, it is necessary to develop models which allow correct prediction of lava flow path and depth. Mathematical modeling based on CFD becomes more and more popular as computing power increases. It is known that parameters of the flow are significantly influenced by the presence of the solid crust, which is formed due to the heat exchange of the lava surface with the atmosphere. In traditional meshbased methods temperature and stress boundary conditions must be specified on an unknown free surface of the flow. In recent years, meshfree numerical methods, which make it possible to overcome the drawbacks of traditional approaches, are actively developed. One of the most popular and established meshless methods is SPH (Smoothed Particle Hydrodynamics) was originally developed for astrophysical applications. Since then it has been modified and successfully applied to a wide range of problems. For a lava flow, important factors influencing the choice of numerical methods are high viscosity, low speed of propagation and large characteristic times of order of days to weeks. Therefore, to use SPH it might be necessary to modify existing methods, and develop new techniques allowing accurate reproduction all physical processes of interest. The aim of this study is to test the capabilities of SPH in application to lava flows in the presence of a temperature dependent viscosity, to determine the problems the method, possible ways of solution, and a further direction of research. For this purpose, a software was developed that implements several different formulations of the SPH method, and several numerical experiments were performed with values of parameters typical for lava flows. It was shown that the results are in a good agreement with known analytical solutions, and the ability of the method to reproduce the effects observed on real lava flows, for example, breaking the crust when a lowviscosity lava is injected into a region filled with highviscosity lava.