A programming device programs a machining control program to be used on a numerical control device for machining an object. A setting unit sets an axial direction of the tool with respect to the data on the machining-target area and sets a deepest position of a tip of the tool with respect to the data on the machining-target area. An extracting unit extracts a surface-machining-target area of the object from the data on the machining-target area based on the set axial direction of the tool, the set deepest position of the tip, and the data on the machining-target area.