Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 127, pp. 1-14. Title: Decay rates of magnetoelastic waves in an unbounded conductive medium Authors: Ruy Coimbra Charao (Federal Univ. of Santa Catarina, Brazil) Jauber Cavalcante Oliveira (Federal Univ. of Santa Catarina, Brazil) Gustavo Perla Menzala (Federal Univ. of Santa Catarina, Brazil) Submitted September 23, 2011. Published October 11, 2011. Math Subject Classifications: 35B40, 35Q60, 36Q99. Key Words: Magnetoelastic waves; exterior domain; localized damping; energy decay.