A modular foam construction system utilizes polystyrene materials and consists of a set of building panels, of predetermined shape, which are configured to define a structure when the panels are arranged and aligned together in accord with a plan or set of instructions. Panels are locked together by coupling together a set of predefined interlock slots, formed into each panel at particular locations, with a set of corresponding interlock keys configured for friction fit insertion into the juxtaposed interlock slots. The keys are oversized to promote a binding surface friction fit between slot and key and both keys and slots are formed with angled sides to promote a pulling force directed towards the bottom of a slot to promote and increase a surface friction fit between slot and key along the slot bottom surface.