The tooth axis estimation program includes, extracting a plurality of points from inputted three-dimensional profile data, the plurality of points indicating a surface of three-dimensional profile data; calculating an arrangement relationship between a point group and a first profile corresponding to a first three-dimensional profile data of a tooth in accordance with moving and/or rotating at least one of the first profile and the point group, the arrangement relationship corresponding to minimum difference between the point group and the first profile, the point group being included in a region of the extracted plurality of points; and specifying a direction of a tooth included in the region in accordance with the calculated arrangement relationship.