Abstract At T = 95 K β-ThBr 4 undergoes a phase transition from a “high-temperature” phase with space group I 4 1/amd to a structure with an incommensurable distortion wave along the crystallographic c axis. The modulation can be thought to consist of a combination of a “rotation” and a “twist” of the Br atoms in the plane perpendicular to the c axis. The EPR spectra at 4.2 K show the characteristic “edge singularities” of the incommensurable structure. A model is presented for the simulation of these spectra. It is based on the “twist” component of the modulation only.