The evolution of dark state of electromagnetically induced transparency(EIT) and the spatial dependence of the steady-state population in a standing wave in a system exhibiting hyperfine splitting were investigated by using the numerical simulation. Two polarization schemes,the circular polarization and the linear polarization,were considered. The combined effect of the individual components was compared with the simple three-level system. Analytical results indicate that the population of the dark state in the circular polarization modes are closer to the simple three-level situation than in the linear polarization modes,and the spatial resolution in the circular polarization modes are better than in the linear polarization modes. The process of evolution also shows that system requires enough interaction time to reach steady-state.