A nesting data generation device that is adapted to generate nesting data for cutting off a part from a work supported by a plurality of support projections, the device comprising: a nesting data generating unit that is adapted to generate the nesting data by arranging a geometry of the part on the work, wherein the nesting data generating unit is adapted to perform, upon arranging the geometry of the part on the work, an avoidance process for avoiding an impediment due to the support projections, characterized in that the nesting data generating unit is adapted to perform, as the avoidance process, a preparation processing for arranging the geometry of the part so as to avoid the part from dropping off from the support projections, in that the nesting data generating unit is adapted to perform, upon arranging the geometry of the part on the work, an outline-expansion process for expanding an outline of the geometry and an arrangement optimizing process for optimizing an arrangement of the geometry within an expanded range of the outline, wherein the nesting data generating unit is adapted to perform said arrangement optimizing process if judging that the part will drop off from the support projections after cutting off the part due to a positional relationship between the center of mass (CoM) of the part and the support projections, and to repeat said arrangement optimizing process until it is judged that a drop-off of the cut part will not occur, in that the nesting data generation device further comprises an outline-restoration processing unit for restoring the expanded outline of the part to its original outline upon judging that a drop-off will not occur, and in that the nesting data generating unit is adapted to perform an NC data generating process for generating NC data based on the generated nesting data. a nesting data generating unit that is adapted to generate the nesting data by arranging a geometry of the part on the work, wherein the nesting data generating unit is adapted to perform, upon arranging the geometry of the part on the work, an avoidance process for avoiding an impediment due to the support projections, characterized in that the nesting data generating unit is adapted to perform, as the avoidance process, a preparation processing for arranging the geometry of the part so as to avoid the part from dropping off from the support projections, in that the nesting data generating unit is adapted to perform, upon arranging the geometry of the part on the work, an outline-expansion process for expanding an outline of the geometry and an arrangement optimizing process for optimizing an arrangement of the geometry within an expanded range of the outline, wherein the nesting data generating unit is adapted to perform said arrangement optimizing process if judging that the part will drop off from the support projections after cutting off the part due to a positional relationship between the center of mass (CoM) of the part and the support projections, and to repeat said arrangement optimizing process until it is judged that a drop-off of the cut part will not occur, in that the nesting data generation device further comprises an outline-restoration processing unit for restoring the expanded outline of the part to its original outline upon judging that a drop-off will not occur, and in that the nesting data generating unit is adapted to perform an NC data generating process for generating NC data based on the generated nesting data.