A turbine engine airfoil structure including an airfoil adapted to extend across a gas passage, and a platform structure defining an endwall located at one end of the airfoil and positioned at a location forming a boundary of the gas passage. A saddle portion is associated with at least one airfoil surface of the airfoil, the saddle portion defining a contour having a first radially outer edge located on the at least one airfoil surface and a second radially inner edge located radially inwardly from the radially outer edge. The contour includes a curvature in a plane extending generally perpendicular to the at least one airfoil surface and passing through the saddle portion, the curvature being radially spaced from the endwall and defining an apex located between the radially outer and inner edges of the saddle portion.