A prototype laser-induced breakdown spectroscopy (LIBS) sensor is tested for the determination of rare earth elements (Eu and Yb) in liquid and solid samples. The sensor head, built using a monolithic passively Q-switched (PQSW) Nd:YAG laser, produced a 1064 nm laser beam with ns pulses and an energy of 4.2 mJ. The measurements show good calibration linearity for both Eu and Yb with R2 values above 0.99 for all analyzed spectral lines in liquid and solid samples. Limits of detection (LODs) obtained were as low as 1 ppm, which are comparable to or better than those reported previously by using table top actively Q-switched systems. This study aims to develop a high sensitivity, field deployable sensor for characterizing existing and new sources of rare earth elements.