Changes in structure and elastic constant with temperature are compared on the melting process for Na and Zn salts of poly(ethylene-co-methacrylic acid) ionomers and nonionic low-density polyethylene. The temperature dependence of the elastic constant was measured by the Brillouin scattering method. Characteristic melting behavior was found from 70 to 100 degrees C for the two ionomers. To elucidate the melting behavior from the structural viewpoint, the structural change in the ion aggregate, the acid dimer-monomer equilibrium, and temperature dependence of the degree of crystallinity were investigated. No correlation was found between these structural changes and the temperature dependence of the elastic constant. Conformational order or the amount of a short trans sequence of polymetheylene chains in the noncrystalline phase was investigated with the Raman method. A correlation between the temperature dependence of the conformational order and that of the elastic constant was found. This was also corroborated by the temperature dependence of the intensity of the disorder LAM (D-LAM) band. The high elasticity of the ionomers was found to be significantly affected by the amount of short trans sequences in the noncrystalline region.