Numerical investigations have been made of the oscillatory entrance flow in a straight pipe, having a bell mouth, perpendicularly to the wall of a large reservoir. Calculations are performed under the conditions of the Womersley numbers of α=2∿20 and the Reynolds numbers of Re=100∿500. The separation at the bell mouth in the outflow term comes to be suppressed with an increase of α. In place of that, for moderate and high α the vortex flow is formed just in front of the bell mouth. The inlet length is appreciably shorter than that for a steady flow and it changes proportionately with Re/α^2,except for sufficiently high α.