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The precipitation kinetics and microtructure in Mg-Sn binary and Mg-Al-Sn ternary alloys are simulated using PanPrecipitation coupled with Mg thermodynamic database and a newly established mobility database of the Mg-Al-Sn ternary system. Both Mg₂Sn and Mg₁₇Al₁₂ precipitates are considered in this work. The obtained kinetic parameters for these two precipitates can be used in the simulation of both individual and concurrent precipitations of Mg₁₇Al₁₂ and Mg₂Sn in Mg-Al-Sn alloys. The simulated microstructure evolution, such as the particle size and number density, are in agreement with experimental data.