Multiple junctions between different grains of a pure material are investigated using the multi-phase field model in 2D and 3D. According to theoretical considerations of the multi-phase field model equations, there may be quasi-static solutions that depend on the ratio of the interface mobilities. Numerical calculations in 2D and 3D indicate that the system always converges to the static solution as described by Young's law independent of the interface mobilities. No quasi-static solutions are found, which is attributed to the necessity of continuous solutions within the interface region of a phase-field model. The effect of interface mobility on the dynamics of the interface angle is discussed.