An association of the finite-difference time domain (FDTD) method together with coupled mode theories (CMTs) has been applied to the study of the bistable properties of whispering gallery mode (WGM) micro-ring resonators. The semi-analytical results obtained are compared with numerical nonlinear full calculations (nonlinear FDTD). It is shown that CMTs allow a good quantitative description of the stationary and dynamical behaviors of the bistability in such micro-resonators. As an example, we treat the case of a polymer micro-ring in a symmetrical dual coupling configuration.