Core-shell Ge/Ge1-xSnx nanowires are considered promising silicon-compatible nanomaterials with the potential to achieve a direct band-gap for optoelectronic applications. In this study, we systematically investigated the formation of this heterostructure in the radial direction by the phase field method coupled with elasticity. Our model simulated the shell growth of the wire, capturing the evolution of both the sidewall morphology and the strain distribution. We predicted the minimum chemical potential driving forces required for initiating the Ge1-xSnx shell growth at given tin concentrations. In addition, we studied the dependences of the shell growth rate on the chemical potential, the tin concentration, the sidewall interface kinetics and the mass transport rate respectively. From these analyses, we identified three sequential stages of the growth: the Stage 1 growth at an accelerated rate, the Stage 2 growth at a constant rate, and finally the Stage 3 growth at a reduced rate scaling with . This research improves our current understanding on the growth mechanisms of heterogeneous core-shell nanowires, and provides useful guidelines for optimizing nanowire synthesis pathways.