The plurality of pieces of low density cellular material, such as foam plastics, form a core panel having opposite side surfaces and with adjacent pieces having opposing edge surfaces extending between the side surfaces. Sheets of flexible material, such as veils or matts or scrim, are adhesively attached to the side surfaces, and portions of one sheet extend between the opposing adjacent edge surfaces for limiting flexing of the panel. The pieces may be tapered, and portions of the one sheet may project between the edge surfaces either partially or fully to form double wall webs. The webs may have flanges adhesively attached to the other sheet on the opposite side. One sheet may also be stretchable in areas not adhesively attached to the pieces to provide for curving the panel from a planar position maintained by the sheet on the opposite side.