The Rensselaer Polytechnic Institute linear accelerator with the enhanced thermal target was used for neutron transmission measurements of rare earth metal samples of holmium, erbium, and thulium and isotopically enriched oxide samples of 166Er2O3 and 167Er2O3 in the energy range from 0.001 to 20 eV. The measurements were done with a 15-m time-of-flight spectrometer and provided high-quality data in the thermal and subthermal region as well as in the low energy resonance region. The effect of paramagnetic scattering on these cross sections is discussed. The data were corrected for paramagnetic scattering, and resonance parameters were obtained by fitting the transmission with the SAMMY multilevel R-matrix code. These results were compared to the ENDF/B-VI evaluation and to other measurements.