Abstract: In this paper,the geometric theory of shaping for blade formed by paraboloid (ruled surface) which is widely used to design axial-radial flow impellers of radial turbomachines is investigated.The wrong conclusions caused by reference[ I Dwhich spread far and wide are corrected herein. The equation of paraboloid having arbitrary position of axis, the sectional curvature of paraboloid and the relation between inlet (or exit)angle and radius are established. On the basis of previous results, the progarmmer for design calculus of shaping of paraboloidal blade may, be worked out.