<p>This study examines the two-dimensional deformation of a functionally graded Green Naghdi (type-III) thermoelastic half-space under hydrostatic initial stress. The material properties of the medium are assumed to vary along two directions. Such type of problem has not been attempted earlier. Using the normal mode technique, analytical expressions for displacement components, temperature distribution, and force stress are derived. The numerical evaluation of these field variables reveals the impact of initial stress and material inhomogeneity on thermoelastic behavior. Graphical representations illustrate the variations in displacement and stress fields, emphasizing the intricate interplay between mechanical and thermal responses. These findings provide valuable insights for stress-strain analysis and the design of advanced engineering materials in thermoelastic applications.</p>