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The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid,whose surface is subjected to a Mode-I crack problem.The problem is studied in the context of the generalized thermoelasticity Lord-S hulman’s (L-S) theory with one relaxation time,as well as with the classical dynamical coupled theory (CD).The normal mode analysis is used to obtain the exact expressions for the displa...,The present paper is aimed at studying the effect of rotation on the general model of the equations of the generalized thermo-microstretch for a homogeneous isotropic elastic half-space solid,whose surface is subjected to a Mode-I crack problem.The problem is studied in the context of the generalized thermoelasticity Lord-Shulman’s (L-S) theory with one relaxation time,as well as with the classical dynamical coupled theory (CD).The normal mode analysis is used to obtain the exact expressions for the displacement components,the force stresses,the temperature,the couple stresses and the microstress distribution.The variations of the considered variables through the horizontal distance are illustrated graphically.Comparisons of the results are made between the two theories with and without the rotation and the microstretch constants.