Abstract: Elastomeric foam blocks are provided for constructing toys and models with a means of attachment of one block to another block in the form of flexible protuberances and cellular receptacles present on all surfaces, so that when one or more blocks are engaged, a clinging force is generated. Furthermore, either independently of, or in collaboration with the above, another means of connecting said blocks is provided by inserting simple pins into the matrix of said foam in any direction and without preformed perforations. The pins are held in place in the perforations created by the insertion of the pins into the foam by the elastomeric forces inherent in the polymeric structure of the foam, and the perforations snap shut upon the removal of the pins, thus allowing the building units to be reused again to construct more toys and models.