The purpose of this thesis was the development and evaluation of different analytical methods for the determination of trace elements in industrial and geological samples. Laser ablation inductively coupled plasma mass spectrometry is known as a fast, almost non destructive, direct solid sampling technique for elemental analysis with high spatial resolution. These benefits could be successfully exploited for samples that require either high speed analysis (rapid screening of boron isotope ratios in nuclear shielding materials), minimum invasive sampling (chert raw materials for provenancing studies in cultural heritage research), or high spatial resolution analysis (metal diffusion in actuator materials). The developed methods were evaluated and compared to common approaches like inductively coupled plasma mass spectrometry, x-ray fluorescence analysis, and electron probe micro analysis. As a result, analysis and data processing protocols have been developed for quality control of boron isotopic composition in special steel samples used for nuclear shielding, for differentiating chert raw materials of similar optical properties by their different trace element pattern (Li, B, Cs), and for plotting and quantifying the diffusion of electrode metals (Ag, Pd) in modern actuator materials (PZT, BNT). Although all developed methods served the purpose several restrictions of LA ICPMS have been observed. The use of high-end equipment (fs-LA-MC-ICPMS) and matrix matched standards could diminish matrix effects and detector limitations when analyzing steel samples. Direct analysis of chert and actuator materials eliminated the need of sample dissolution by microwave-assisted digestion with concentrated acids, although detection limits of liquid ICPMS could not be reached. Micro inhomogeneity of all samples was observed, which was compensated by multiple analyses on steel and chert but could be utilized for the determination of diffusion in actuator materials.