A limitation of the Swift test for drawability is that, being based on the drawing of a round cup, it cannot bo applied to non-circular cups. To be applicable to non-circular cups the definition of drawability, and the test or tests based on it must entail a more generalized concept than the largest drawing ratio. Such a generalized definition, is proposed, and it is derived from the basic ideas in the Swift test. A measuro for the draw-in, analogous to the surface strain, is proposed to replace the drawing ratio and the boundary of the product is defined both for specifying the stage at which the drawing operation is completed and for the determination of the draw-in. The choice of the blank size, which is simple in the Swift teat, becomes more complex in the case of cups with boundaries of different sizes. In the non-circular cups, the maximization of the draw-in, which is basic and essential to the concept of drawability, can be achieved by choosing the shape and the orientations of the blank, as well as the size. Actual examples are shown of the variation of drawability with the size of the blank, the shape of the blank, the orientation of the blank, the size of the boundary of the product, as well as with the shape of the cup.