An embroidery data processing apparatus is constructed to execute calculation for forming a plurality of circles with different radii concentrically around a central point, extract circles and arcs that fall within the embroidery region from the thus formed circles, and determine stitch points on the circles and arcs that fall within the embroidery region. The thus created stitching data features thread flows along the arcs and concentric stitches with a new texture, not existing before, can be created.