A strain wave gearing having 3-dimensional meshing tooth profile comprising: a rigid internally toothed gear; a flexible externally toothed gear (3, 3A) coaxially arranged inside the internally toothed gear; and a wave generator fitted into the externally toothed gear (3, 3A), wherein the externally toothed gear (3, 3A) has a flexible cylindrical body; a diaphragm extending in a radial direction from a rear end of the cylindrical body; and external teeth formed on an outer circumferential surface portion on a side of a front end of the cylindrical body, the front end being an open end, the cylindrical body of the externally toothed gear (3, 3A) is flexed into an elliptical shape by the wave generator, and the external teeth are meshed with internal teeth of the internally toothed gear on both ends in a direction of a major axis of the elliptical shape, a flexion amount of the external teeth increases from an external-teeth inner end at a side of the diaphragm toward an external-teeth outer end at a side of the open end along a tooth trace direction of the external teeth, the flexion amount being in proportion to a distance measured from the diaphragm, the internal teeth have a tooth profile that is a same at each position along a tooth trace direction of the internal teeth, and the external teeth have a tooth profile configured so that: a tooth-tip tooth thickness (D2a, D2e) thereof gradually decreases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth; characterized in that the tooth-tip thickness(D2a, D2e) decreases in a concave-curvilinear or a convex-curvilinear manner along the tooth trace direction of the external teeth, so that a pressure angle (αa,αe) at a pitch point thereof gradually increases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth. a rigid internally toothed gear; a flexible externally toothed gear (3, 3A) coaxially arranged inside the internally toothed gear; and a wave generator fitted into the externally toothed gear (3, 3A), wherein the externally toothed gear (3, 3A) has a flexible cylindrical body; a diaphragm extending in a radial direction from a rear end of the cylindrical body; and external teeth formed on an outer circumferential surface portion on a side of a front end of the cylindrical body, the front end being an open end, the cylindrical body of the externally toothed gear (3, 3A) is flexed into an elliptical shape by the wave generator, and the external teeth are meshed with internal teeth of the internally toothed gear on both ends in a direction of a major axis of the elliptical shape, a flexion amount of the external teeth increases from an external-teeth inner end at a side of the diaphragm toward an external-teeth outer end at a side of the open end along a tooth trace direction of the external teeth, the flexion amount being in proportion to a distance measured from the diaphragm, the internal teeth have a tooth profile that is a same at each position along a tooth trace direction of the internal teeth, and the external teeth have a tooth profile configured so that: a tooth-tip tooth thickness (D2a, D2e) thereof gradually decreases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth; characterized in that the tooth-tip thickness(D2a, D2e) decreases in a concave-curvilinear or a convex-curvilinear manner along the tooth trace direction of the external teeth, so that a pressure angle (αa,αe) at a pitch point thereof gradually increases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth. a tooth-tip tooth thickness (D2a, D2e) thereof gradually decreases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth; characterized in that the tooth-tip thickness(D2a, D2e) decreases in a concave-curvilinear or a convex-curvilinear manner along the tooth trace direction of the external teeth, so that a pressure angle (αa,αe) at a pitch point thereof gradually increases from the external-teeth outer end toward the external-teeth inner end along the tooth trace direction of the external teeth.