A high-pressure neutron diffraction study was conducted on polycrystalline samples of the two known polymorphs of 2,4,6-trinitrotoluene [monoclinic (m-) and orthorhombic (o-) TNT] under hydrostatic conditions. Isothermal equations of state were obtained for both polymorphic forms. Neither polymorph was observed to undergo a phase transition in the pressure region 0-5 GPa, with both polymorphs displaying smooth compression behavior across the pressure range. This differs somewhat from previous XRD and Raman spectroscopy investigations in which discontinuities were observed in the P-V curves and spectral changes were reported at ~2 GPa. The high-pressure response of these materials is supported by dispersion-corrected DFT calculations which, while overestimating the experimental bulk moduli, give excellent agreement with the observed smooth compression response of both phases.