The present paper attempts to investigate the propagation of plane waves in an isotropic elastic medium under the effect of initial stress and temperature-dependent properties. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (J. Thermal Stresses, 30, 231 (2007)). Normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress, and the strain components. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made with the results predicted by different theories (Lord–Shulman theory, the theory of thermoelasticity type III, and the three-phase-lag model) in the absence and presence of the initial stress as well as the case where the modulus of elasticity is independent of temperature.