An insulating panel structure has an inner surface for attachment to a building exterior and an outer surface for attachment to cladding material. The panel structure has external stringers for attachment of the cladding, connectors extending perpendicularly from the inner surface to the external stringers to transmit compressive forces from the cladding to the building, lateral connectors that run diagonally upward from the external stringers to the inner surface to transmit tensile forces from the weight of the cladding to the building, and insulating foam embedded between the panel inner and outer surfaces. A panel application method includes providing panels with tubular connectors and providing expansible fingers insertable into the tubular connectors and mounted on a movable frame, inserting the fingers into the tubular connectors, expanding them to grip the tubes and panels, moving the frame with expanded fingers and panel to a job site, attaching the panel to a building while being held with the expanded fingers, and contracting and retracting the fingers from the attached panel.