The free-surface flow of a horizontal fluid layer due to an impulsively started point sink at the bottom wall is analytically studied by employing a power series expansion in time. The full surface elevation is calculated using symbolic calculator. Amplitude expansion is also used for extracting free-surface oscillation at the lower Froude number which is defined with respect to the sink strength and the initial submergence depth. To enlarge the radius of convergence of the perturbation series, $Pad\acute{e}$ approximant is adopted.
A new criterion for the critical Froude number for the dip formation is proposed, and the critical value is estimated to be about 0.13, which is lower than the previous ones.
