Purpose The aim of this work is to study porous thermo-elastic behavior in a half-space elastic micro-stretch media enveloped in an unbounded inviscid liquid with a magnetic field, utilizing three-phase lag model (3PHL) and Green–Naghdi theory of type III (G–N III). Methods The analytical technique used to obtain the ordinary differential equations was normal mode analysis. The Gauthier composite element is employed in an implementation to start comparing the observations—magnetic field on thermo-microstretch elastic porous medium completely covered in the endless fluid of G–N III theory with those for the model of 3PHL. Results The magnetic field has been observed to make a significant impact over all physical quantities. Also, comparisons have been made for four various frequency values which explained that the frequency has an important role on the physical quantities. Conclusion Overall, the research on the magnetic field effect on thermo-micro-stretch porous media immersed in a liquid has several potential practical implications and engineering applications in various fields, such as biomedical, environmental, chemical, and energy engineering.