Unsteady motions of sink flows having a free surface are studied numerically. First, for a line sink, the results on dip formation are obtained and corroborate Tyvand's series solution [Phys. Fluids A4, 671 (1992)], except for small disagreements for large t owing to the finiteness of the calculational domain in our numerical approach. Next, to investigate the drain-size effect in dip formations, free-surface hows due to a sink array are considered. The effective sink strength q(eff) is found to be approximated by q(eff)/q(0) = 1 - alpha(d/2)(beta), alpha approximate to 0.27, beta approximate to 1.86, q(0) is the total sink strength, and d is the array length.