Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry (LA-ICP-MS) is a method excellently suited for the laterally resolved analysis of trace elements in tissue samples. Information about the distribution of metals in biological samples - either endogenous or exogenous to an organism - can reveal important information about biological processes. Within this PhD thesis, simple and accurate quantification strategies of trace elements in tissue samples could be successfully developed. Single- as well as multi-element quantification of trace metals could be achieved. In further experiments, LA-ICP-MS was used in parallel with Laser Induced Breakdown Spectroscopy (LIBS); such Tandem LA/LIBS setup showed to also allow access to biological bulk elements such as carbon, oxygen, or hydrogen in the laterally resolved analysis of tissues. Besides developing and optimizing approaches for quantification and extending the multi-element capabilities, also the topic of image quality was addressed. It was possible to define a metric which is capable of quantitatively defining image quality of elemental distribution images - a useful feature for optimization of the instrumental parameters for a measurement. Developed analytical procedures could be successfully applied to questions of medical relevance. Especially investigations on platinum distributions in tumor tissues delivered results which excellently complement traditional approaches for diagnosing drug uptake and efficacy.