Lead cylinders are placed as hexagonal array in the background matrix material, polyethylene. The lattice length is 10cm. We discuss the band gap structure by selecting various size of lead cylinders. As suggested by Huang and Sun, they showed that the range of the gap could be significantly increased by an insertion of a compliant layer [16]. Here, in our investigation, we also consider a coated cylinder, embedding a fluid-like material between the inclusion, lead, and the matrix, polyethylene, Fig 1(b). We also discuss the band structure for the latter coated cylinder configuration.