Abstract: This paper combines L-S thermoelasticity with acoustoelasticity based on  continuum mechanics and analysis process of rational extended thermodynamics to establish the basic framework of L-S thermoacoustoelasticity, including four components: kinematics, mechanics and thermodynamics, constitutive equations and evolution equations, and fundamental field equations. In the kinematic part, Lagrangian description and Eulerian description are distinguished, as well as three different states and configurations, while two types of transition processes from the natural state to the initial state are defined for the case of thermoacoustoelasticity; In the mechanics and thermodynamics part, the laws of conservation of mass, conservation of momentum, conservation of angular momentum, conservation of energy, and the entropy production inequality are given, which lead to the limitations of classical irreversible thermodynamics; In the part of the constitutive equations and evolution equations, the principle of extended irreversible thermodynamics is introduced, and the constitutive equations and evolution equations of thermoacoustoelasticity from the natural state to the initial state and those from the initial state to the final state are derived based on the process of rational extended thermodynamics, taking heat flux as the constitutive independent variable and considering the correlation of heat flux with strain and temperature; In the last part, the equations of motion and the first-order velocity-stress- heat flux-temperature differential equations for numerical simulations are given.

Key words: L-S theory, thermoelasticity, acoustoelasticity, continuum mechanics, rational extended thermodynamics