A typical time evolution of the phase mixing phenomena is clarified for an idealized model from the standpoint of the local analysis. The model equations are taken from those of the Alfvén type standiing waves in a square region subject to a uni-directional magnetic field and to the effect of small diffusivity in which the Alfvén velocity changes with the magnetic lines offeree. These equations are solved by the use of the WKB method of solution combined with a small perturbation method with respect to the diffusivity. The results gives the time evolution (1) in the initial period in which mutually independent standing waves along each magnetic lines of forces are modulated by the phase mixing effect and (2) in the final period in which these modulated waves are damped off to become asymptotic steady state.