This paper concerns with the study of wave propagation in fibre reinforced anisotropic half space under the influence of temperature and hydrostatic initial stress. Lord-Shulman theory is applied to the heat conduction equation. The resulting equations are written in the form of vector matrix differential equation by using Normal Mode technique, finally which is solved by Eigen value approach. Keywords: eigenvalue, generalized thermoelasticity, normal mode, vector-matrix differential equation. 1. Introduction Fibre-reinforced composite (FRC) materials are usually low weight and high strength used in construction engineering. The physical property of FRC material is governed by the theory of elasticity for different materials with the direction along the direction of fibre. Green [1] studied wave propagation in anisotropic elastic plates. Abbas and Othman [2] discussed the distribution of wave propagation under …