In this paper, the equations representing the one-dimensional, linearized, simultaneous, coupled problem of magnetothermoelasticity are arranged in the form of a matrix differential equation in the Laplace transform domain. The problem is then converted to an algebraic eigenvalue problem and solved in the same domain. The results obtained can be used to solve a broad class of problems in magnetothermoelasticity. Applications to problems pertaining to a half-space and a layer are presented. The results obtained for some special cases are compared to the results in the literature.