This work provides a measurement procedure for the complete digestion of rock samples containing refractory minerals such as zircon and chromite. Their dissolution by wet acid digestion is often incomplete but, although providing complete digestions, alkali fusion techniques can result in solutions with a high blank and total dissolved solid content. It was established by the systematic study with reference material trachyandesite MTA-1 that a 1:6 sample to sodium peroxide (Na2O2) ratio is conservative for the complete digestion and recovery of all the analytes especially those contained in zircon. The sample decomposition time was 120 min for the zircon-bearing rhyolite reference material MRH-1. Complete digestion of chromite was obtained in the harzburgite RM MUH-1. The sample solutions were stable for at least 1 year. Accurate measurements of SiO2, Al2O3, TiO2, P2O5 and K2O could be made with ICP-MS by not discarding the supernatant of the sinter solution and by using geological reference materials for external calibration. HF digestions are slow, not universal, and may form new mineral/phases that are insoluble under high temperature conditions. The validated sample decomposition procedure combined with ICP-MS presents an alternative to the use of HF in routine analysis of difficult to digest geological materials.