Sn is one of the promising Li ion battery anode materials with high theoretical capacity and mechanical properties that allow for effective relaxation of Li diffusion-induced stresses. Sn is a low melting point metal with a low modulus and strength and has the ability to relax stresses via plasticity and creep deformations. In this study, concentration-dependent material properties are used in numerical simulations to model the Li diffusion-induced stress evolution in Sn micropillars. Simulation results using concentration-dependent material properties resulted in a completely different failure mode in comparison to that of concentration-independent simulation results. Tensile hoop stress needed for crack propagation was analyzed to be at the core for concentration-independent material properties, and switched to being at the surface for concentration-dependent simulation results. In addition, by incorporating these maximum tensile DIS results, the critical size for the failure of Sn micropillars was determined to be 5.3 mm at C/10 charging rate. This was then correlated with experimental observations, where fracture occurred in Sn micropillars with sizes larger than 6 mm, while 4.4 mm sized Sn micropillars survived the lithiation cycle.