An outer shell for a composite building panel includes a tongue and correspondingly shaped groove formed on opposite side edges thereof for interlocking like panels to form a wall. The tongue extends outwardly from the side edge of the panel and has a forward portion with parallel sides which are straight and parallel to a central plane of the panel. The tongue has an intermediate portion that tapers outwardly from the parallel sides toward a side face of the panel. The tongue has a rearward portion with parallel sides. Inner faces of the groove are configured for close engagement of the forward and rearward portions of the tongue.