BACKGROUND: Mixed acid open acid dissolution and alkali fusion methods are the two main dissolution methods for determination of rare earth and refractory elements in geological samples by inductively coupled plasma-mass spectrometry (ICP-MS). However, the composition of geological samples is complex. For special elements and special samples, the traditional acid-dissolving method will cause incomplete digestion of some elements, which makes the measurement results inaccurate. The operation process of the alkali fusion method is cumbersome. The solution has high salinity, which can easily cause matrix interference and block the sample introduction system. OBJECTIVES: To improve the traditional four-acid and penta-acid systems in the determination of rare earth elements. METHODS: The hydrofluoric acid-nitric acid-sulfuric acid open acid solution system was used to determine the 15 rare earth elements by using the national standard material to prepare a standard curve. At the same time, the lithium metaborate alkali fusion method was improved. The sample was extracted with lithium metaborate alkali, and the solution was added to the alkaline condition by adding sodium hydroxide. The measured element was coprecipitated with lithium metaborate, and the flux was separated and filtered, and then reconstituted with nitric acid. Nineteen elements such as rare earth and lanthanum zirconium were measured. RESULTS: The relative deviations between the measured value and the certified value of the two dissolution methods were 1.09%-9.30%. The results of determination of Nb, Ta, Zr and Hf by mixed acid open dissolution method and rare earth element by lithium metaborate alkali fusion method were compared with those of another laboratory that used closed acid dissolution methods. The relative deviations between the two groups were 0.13%-15.32%. CONCLUSIONS: The mixed acid open dissolution method is suitable for the determination of rare earth elements in geological samples, whereas the lithium metaborate alkali fusion method is not only suitable for the determination of rare earth elements and Nb, Ta, Zr and Hf in geological samples, but also for the determination of Nb, Ta, Zr and Hf in ancient high pressure metamorphic rock samples and the sample with a high Al content.