Magnetoelastic investigations allow tests of microscopic models and theories that include crystal electric field and magnetic exchange interactions. In addition, aspects of the technical methods are of practical interest. Rare earth based antiferromagnets show a wide variety of magnetically ordered states, and transitions between them can be detected very precisely using capacitive dilatometers that sense magnetostriction. Because of the small size ( 22 mm) of the dilatometer it can be operated at low temperatures in the highest steady magnetic fields available at the NHMFL Tallahassee. With care, a resolution of 10-6 in dl/l can be realized. The measurements of longitudinal as well as transverse components of the striction tensor of SmCu2 in a 33 T magnet show a strong distortion in the ac plane in fields along the easy-axis b direction. The lattice parameters a and c change by about 3×10-3 at 25 T. This is correlated with the field-induced transition from an antiferromagnetic to a ferromagnetic state. In fields parallel to the c axis no giant magnetostriction, as is known for other RCu 2 compounds, could be detected.