We introduce a new conserved quantity, Normalized Energy Density (NED), alternative to the conventional definition of energy for a layered structure in a 2D SH problem. NED is defined by the average of power of a half transfer function multiplied by the impedance, and the conservation across the material interface is analytically proved for a two-layered case. For three, four, and ten-layered cases, the conservation is examined by applying the Monte Carlo simulation method, and then NED is supposed to be conserved through the layers. (C) 2011 Elsevier B.V. All rights reserved.