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A multiphysics numerical approach based on a coupling of heat conduction equation, mechanical field (effect of gravity), and phase-field equations is proposed as an alternative to predict the microstructure evolution of 316L stainless steel during the pressureless solid-state sintering process. In this context, a numerical model based on the finite element method has shown to be suitable for evaluating the impact of the thermal field, as the activation force of the sintering process, on the microstructure field evolution and, in turn, the impact of the evolution of phase field variables on the material properties. The model was validated by comparison with literature results and applied to simulate the microstructure evolution for different sintering temperatures and particle sizes to evaluate the influence of these parameters on microstructure evolution. The results proved that model can be used to analyze the microstructure evolution, both from a quantitative and quality point of view, which makes it suitable for evaluating the impact of sintering parameters on material properties.