Abstract : This paper describes the development of a numerical homogenization tool adapted to TATB-based pressed explosives. This is done by combining virtual microstructure modeling and Fourier-based computations. The polycrystalline microstructure is represented by a Johnson-Mehl tessellation model with Poisson random nucleation and anisotropic growth of grains. Several calculations are performed with several sets of available data for the thermoelastic behavior of TATB. Good agreement is found between numerical predictions and experimental data regarding the overall thermal expansion coefficient. The results are shown to comply with available bounds on polycrystalline anisotropic thermoelasticity. Finally, the size of the representative volume element is derived for the bulk, shear and volumetric thermal expansion moduli.