Three-dimensional (3D) enveloping grasps for dexterous robotic hands possess several advantages over other types of grasps. This paper describes a new method for kinematic 3D enveloping grasp planning. A new idea for grading the 3D grasp search domain for a given object is proposed. The grading method analyzes the curvature pattern and effective diameter of the object, and grades object regions according to their suitability for grasping. A new approach is also proposed for modeling the fingers of the dexterous hand. The grasp planning method is demonstrated for a three-fingered, six degrees-of-freedom, dexterous hand and several 3D objects containing both convex and concave surface patches. Human-like high-quality grasps are generated in less than 20 s per object.