We study the thermoelastic response of a microstretch half-space immersed in an unbounded, inviscid fluid under initial stress; the medium is studied using the Green–Naghdi theory (G-N III) and the three-phaselag (3PHL) model. The relevant equations were formulated in the context of the G-N III theory and the 3PHL model. We obtain an analytical solution to the problem using normal mode methods. Magnesium crystal elements are used as an application to compare the initial stress predictions of a microstretch thermoelastic immersed in an infinite liquid of G-N theory type III with those of the 3PHL model. It was found that the initial stress has a significant influence on all physical quantities. The three wave number values are also compared. It is concluded from the present contribution that some advanced microstretch thermoelastic systems deserve study