The present invention relates to an area cutting method for cutting the interior of an area (AR) by moving a tool along a plurality of offset paths (CPT1, CPT2, . . . CPTn) successively offset in an inward direction from a closed curve (OLC) specifying the area (AR). In accordance with the area cutting method, the centroid (W) of the area is found and a check is performed as to whether the centroid lies inside the area. It is also checked whether line segments (L1, L2, L3, . . . ) connecting the centroid with the apices (P1, P2, . . . , P10) of the area intersect the closed curve (OLC'). If the centroid (W) lies within the area and none of the line segments intersect the closed curve, the area is not divided into a plurality of convex polygons even if the area is a concave polygon. Instead, each line segment is partitioned into a predetermined number of partitions and cutting is performed by moving the tool along a plurality of closed paths (CPT1-CPTn) connecting consecutive partitioning points Pi1 through Pi10 (i=a, b, . . . n) of the line segments.