Background/Introduction Thermoacoustic behavior in elastic media is a complex phenomenon influenced by multiple physical fields, particularly under external stimuli such as laser heating and magnetic fields. Conventional thermoelastic models often overlook the coupling effects of acoustic pressure, two-temperature effects, and magneto-thermal interactions, which are essential for accurate prediction at micro- and nano-scales. Purpose This study aims to develop an advanced thermoelastic framework that integrates acoustic pressure and two-temperature theory to analyze the propagation of thermoacoustic-mechanical waves in a homogeneous, isotropic, elastic half-space subjected to laser irradiation and a constant magnetic field. Methods Using the linear theory of two-temperature thermoelasticity, the governing equations were formulated incorporating both conductive and thermodynamic temperature. The model accounts for magnetic and acoustic pressure effects. Normal mode analysis was applied to solve the resulting boundary value problem. Analytical expressions for displacement, temperature fields, acoustic pressure, and thermal stresses were derived. Results The results reveal how laser pulse intensity, thermal relaxation times, and magnetic field strength influence the distribution of thermal and mechanical fields. Acoustic pressure significantly modifies the stress and displacement profiles, while the magnetic field alters wave propagation characteristics. Graphical results illustrate the variations of key physical parameters across the domain. Conclusions The proposed model successfully extends the general theory of thermoelasticity to include acoustic pressure effects under magneto-thermal conditions. It provides deeper insights into the interactions between laser-induced heating, magnetic fields, and acoustic responses in elastic materials, making it valuable for applications in sensing, nondestructive testing, and material diagnostics.