Electronic Journal of Differential Equations, Vol. 2005(2005), No. 140, pp. 1-15. Title: Initial boundary value problem for a system in elastodynamics with viscosity Author: Kayyunnapara Thomas Joseph (Tata Institute, Mumbai, India) Abstract: In this paper we prove existence of global solutions to boundary-value problems for two systems with a small viscosity coefficient and derive estimates uniform in the viscosity parameter. We do not assume any smallness conditions on the data. Submitted June 10, 2005. Published December 5, 2005. Math Subject Classifications: 35B40, 35L65. Key Words: Elastodynamics equation; viscosity; initial boundary value problem.