Abstract: A set of building blocks useful for constructing model structures includes a plurality of building blocks comprising block bodies and block interconnecting structure. The block interconnecting structure releasably locks each block to one or more adjacent blocks by resisting the blocks being pulled apart from each other. The interconnecting structure does provide, however, a limited amount of lateral play between the blocks so that the interconnected blocks may be moved laterally with respect to each other. The interconnecting structure preferably comprises one or more connecting elements installed into respective apertures in the block bodies. Some blocks have connecting elements with both an inserting end that projects above an outer surface of the block body and a receiving end disposed within the aperture. Other blocks have connecting elements having only a receiving end.