Abstract : At low temperatures β-ThCl4 undergoes a structural phase transition (Tc=70 K) to an incommensurate structure which can be described as a transverse sinusoidal displacement of the chloride ion positions in a plane perpendicular to the C4 axis of the crystal. These static, atomic displacements induce a continuous distribution of crystal field strengths acting on U4+ embedded in the host matrix. The peculiar lineshapes recorded on absorption spectra and the apparently continuous character of fluorescence energies observed in selective excitation experiments are consistent with a continuous distribution of U4+ sites. In this paper we report a study of the interactions of Stark energy levels belonging to the 1I6 multiplet of U4+ (in the 19 700-19 500 cm-1 energy range) in a magnetic field. Absorption and selectively excited emission spectra recorded at 4.2 K have been used to build an energy level model. The calculated profile of the absorption bands in a magnetic field B parallel to the 〈111 〉 orientation is compared to the experimental observed ones.