1. A modeling device comprising: a data obtainer configured to obtain, from a measurement device for performing three-dimensional measurement of a three-dimensional object, multiple pieces of measurement data each indicative of a set of coordinates in three dimensions and individually corresponding to multiple measurement points belonging to the three-dimensional object; a surface extractor configured to generate mathematical formulae representing surfaces constituting the three-dimensional object by use of the multiple pieces of measurement data; and a modeler configured to generate a shape model representing the three-dimensional object from the mathematical formulae, the surface extractor being configured to: determine, by use of mathematical formulae which are of the mathematical formulae and represent a first surface and second surfaces surrounding the first surface, of the surfaces of the three-dimensional object, boundaries surrounding the first surface; extract, from measurement points which are of the multiple measurement points and belong to the first surface, measurement points relating to a region which is inside the first surface and has a predetermined width from the boundaries; and redetermine the mathematical formula representing the first surface by use of the extracted measurement points.