Abstract: A method for the complete dissolution of "hard to dissolve" mineral samples, such as lunar and geological samples, wherein milligram amounts of a sample in particulate form is successively mixed while heating with small amounts of hydrofluoric acid and a mixture of sulfuric acid and distilled, demineralized water. Heating of the resulting solution is continued until its volume is reduced to about 2 milliliters after which the solution is rapidly cooled to room temperature. After adding a small amount of distilled, demineralized water, it is heated while swirling to provide a crystal clear solution. When dissolving lunar or other samples containing beryllium and chromium, an amount of a solution of sodium hydroxide is added to the crystal clear solution that is sufficient to bring the pH of the solution to about 2.5. The method makes it possible to completely dissolve mineral samples rapidly and efficiently for subsequent accurate chemical analysis.