The magnetoelastic (MEL) stresses of single crystal Ho and Er thin films are measured at low temperatures and in applied magnetic fields up to 12 T by means of a capacitive cantilever technique, to determine the irreducible second-order basal plane MEL stressB&ggr;,2. For Ho, the data are well fit by the Callen and Callen law, givingB&ggr;,2=0.29 GPa at 0 K and 12 T, slightly larger than the bulk value, which suggest a negligible effect of the clamping onB&ggr;,2. For Er, the lack of saturation prevents the determination of the single-ion contribution toB&ggr;,2at 0 K. Nevertheless, its sign, which is negative, agrees with the theoretical crystal field prediction. ©1998 American Institute of Physics.