A cup-type strain wave gearing comprising: a rigid internally toothed gear ; a flexible externally toothed gear ; and a wave generator , wherein the externally toothed gear has: a cylindrical body that is flexible in a radial direction; a diaphragm extending toward a center-axis line of the cylindrical body from one end of the cylindrical body , the one end being a rear end thereof; a rigid annular or discoid boss formed in a center-side portion of the diaphragm ; and external teeth formed on an outer circumferential surface portion of the cylindrical body at a side of the other end of the cylindrical body , the other end being an open end of the cylindrical body , and the wave generator is configured to flex an open-end side portion of the cylindrical body where the external teeth are formed, into an elliptical shape to form meshing sections meshing with the internally toothed gear at a plurality of positions separated in a circumferential direction, and wherein, in a state before being flexed by the wave generator , an inside diameter (D) of the cylindrical body is such that a rear-end inside diameter at the rear end is smallest and gradually increases from the rear end toward the open end , an outside diameter of the cylindrical body is such that a rear-end outside diameter is smallest and gradually increases from the rear end toward the open end , characterised in that in a state being flexed by the wave generator , the open end of the cylindrical body has an elliptical inner circumferential surface, a minor diameter (D1) of which is the same as the rear-end inside diameter (D) of the cylindrical body . a rigid internally toothed gear ; a flexible externally toothed gear ; and a wave generator , wherein the externally toothed gear has: a cylindrical body that is flexible in a radial direction; a diaphragm extending toward a center-axis line of the cylindrical body from one end of the cylindrical body , the one end being a rear end thereof; a rigid annular or discoid boss formed in a center-side portion of the diaphragm ; and external teeth formed on an outer circumferential surface portion of the cylindrical body at a side of the other end of the cylindrical body , the other end being an open end of the cylindrical body , and the wave generator is configured to flex an open-end side portion of the cylindrical body where the external teeth are formed, into an elliptical shape to form meshing sections meshing with the internally toothed gear at a plurality of positions separated in a circumferential direction, and wherein, in a state before being flexed by the wave generator , an inside diameter (D) of the cylindrical body is such that a rear-end inside diameter at the rear end is smallest and gradually increases from the rear end toward the open end , an outside diameter of the cylindrical body is such that a rear-end outside diameter is smallest and gradually increases from the rear end toward the open end , characterised in that in a state being flexed by the wave generator , the open end of the cylindrical body has an elliptical inner circumferential surface, a minor diameter (D1) of which is the same as the rear-end inside diameter (D) of the cylindrical body . <EOS>