Transitions of flow in periodically contracted-expanded channel and pressure characteristics are numerically investigated for effects of the channel geometries by using finite difference method. The flow fields are assumed to be two-dimensional and periodically fully developed. Steady state solution of the flow is obtained for relatively small Reynolds number, whereas it becomes unstable and self-sustained oscillatory one at the critical Reynolds number depending on the channel geometry. The critical Reynolds numbers are obtained for various channel geometries. It is found that the self-sustained oscillatory flow occurs as a result of Hopf bifurcation driven by a Tollmien-Schlichting wave. Moreover, it is seen that the pressure drop decreases for the expanded channel geometry compared with that of parallel plate flow for the subcritical Reynolds numbers, while increase for the supercritical Reynolds numbers. On the other hand, the pressure drop for the contracted channel is always larger than that of the parallel plate flow.