The problem of the modernization of a LAMAS-10M laser desorption/ionization time-of-flight mass spectrometer was considered, and the methodological fundamentals of the quantitative analysis of bulk and powdered samples by laser desorption/ionization time-of-flight mass spectrometry were discussed. Basic modifications of certain spectrometer units were described, and the reproducibility and accuracy that can be attained using these modifications were estimated. The possibility of the quantitative analysis of bulk samples was demonstrated. These studies were performed using bulk and powdered standard reference materials. In determining precious metals in geological samples, the detection limit for powdered samples was (20–50) × 10−9. The relative standard deviation for the repeatability of the results (RSD) of the bronze standard reference sample “bronza 663” was in the limits RSD = 0.06−0.4% for the major component and 0.5–4.5% for the elements present in percent concentrations. It was shown that the majority of analytes can be determined at a semiquantitative level without using standard reference materials. The key problems of laser desorption/ionization time-of-flight mass spectrometry were considered and methods were proposed to solve these problems. Ways to further improvement of the characteristics of the mass spectrometer were demonstrated.