A cup-shaped flexible externally toothed gear (3; 20) for use in a cup-type strain wave gearing, in which the cup-shaped flexible externally toothed gear (3; 20) is deformed by a wave generator into an ellipsoidal shape and is partially mesh with a rigid internally toothed gear, the cup-shaped flexible externally toothed gear (3; 20) comprising: a flexible cylindrical body (11; 21) having a first end and a second end in a direction of a center axis line (11b; 21a); a diaphragm (12; 22) extending radially inward from the first end of the cylindrical body (11; 21); a rigid boss (13; 23) formed integrally in a center portion of the diaphragm (12; 22); and external teeth (14, 24) formed on an outer peripheral surface portion of the second end of the cylindrical body (11; 21), wherein when cut along a plane including the center axis line (11b; 21a), an inside end face profile of the rigid boss (13; 23) and the diaphragm (12; 22) is defined by an inside straight line perpendicular to the center axis line (11b; 21a), and an outside end face profile of the diaphragm (12; 22) is defined by a first concave circular arc having a first radius, a second concave circular arc having a second radius, and an inclined straight line; wherein the first concave circular arc is smoothly connected at one end thereof to a parallel straight line parallel to the center axis line (11b; 21a) and defines an outer peripheral surface of the rigid boss (13; 23), the second concave circular arc is smoothly connected at one end thereof to the other end of the first concave circular arc, and the inclined straight line is smoothly connected to the other end of the second concave circular arc and is inclined toward the inside straight line, and wherein the second radius of the second concave circular arc is larger than the first radius of the first concave circular arc, and a thickness of the diaphragm (12; 22) is gradually decreased from a side of the rigid boss (13; 23) to a side of the cylindrical body (11; 21), characterized by that a maximum value of a pitch circle diameter of the external teeth (14, 24) is 40 mm, and a minimum value of the first radius of the first concave circular arc is 0.2 mm. a flexible cylindrical body (11; 21) having a first end and a second end in a direction of a center axis line (11b; 21a); a diaphragm (12; 22) extending radially inward from the first end of the cylindrical body (11; 21); a rigid boss (13; 23) formed integrally in a center portion of the diaphragm (12; 22); and external teeth (14, 24) formed on an outer peripheral surface portion of the second end of the cylindrical body (11; 21), wherein when cut along a plane including the center axis line (11b; 21a), an inside end face profile of the rigid boss (13; 23) and the diaphragm (12; 22) is defined by an inside straight line perpendicular to the center axis line (11b; 21a), and an outside end face profile of the diaphragm (12; 22) is defined by a first concave circular arc having a first radius, a second concave circular arc having a second radius, and an inclined straight line; wherein the first concave circular arc is smoothly connected at one end thereof to a parallel straight line parallel to the center axis line (11b; 21a) and defines an outer peripheral surface of the rigid boss (13; 23), the second concave circular arc is smoothly connected at one end thereof to the other end of the first concave circular arc, and the inclined straight line is smoothly connected to the other end of the second concave circular arc and is inclined toward the inside straight line, and wherein the second radius of the second concave circular arc is larger than the first radius of the first concave circular arc, and a thickness of the diaphragm (12; 22) is gradually decreased from a side of the rigid boss (13; 23) to a side of the cylindrical body (11; 21), characterized by that a maximum value of a pitch circle diameter of the external teeth (14, 24) is 40 mm, and a minimum value of the first radius of the first concave circular arc is 0.2 mm.