Characteristics of the pump in a square channel using the Weis-Fogh mechanism, which is the lift generation mechanism in the hovering flight of small insects, are studied in this paper. The wing motion of this mechanism is changed from the previous reciprocal type to a rotary type, which is considered to be simpler to apply to hydraulic machinery. A two-dimensional model of the above pump is proposed and the force on the wing is calculated by the singularity method. The pressure difference between the two points in front and behind the wings, the torque and the flow field around the wings are also shown. This model works as a pump or as a water turbine. The pressure rise increases as the number of wings or the flow coefficient increases.