A structural insulated laminated construction panel for building structures is described. The panel comprises a rigid core material layer of expanded polymeric material having opposed flat parallel surfaces. An outer skin is adhesively secured to one of the flat surfaces and an inner skin is adhesively secured to the other of the flat surfaces. The core material layer has a density of about 2 lbs/cubic foot. The core material is preferably an expanded polystyrene material. A building structure is constructed from such panels used as exterior and interior wall panels, floor panels and roof panels.