This dissertation elaborates the computational aspects of the calculation of measurement uncertainty. Based on a fundamental analysis of the information provided by a measurement, different evaluation methods are reviewed. Based on this analysis, the Monte Carlo method and its computational aspects are elaborated and applied to different real life measurements from chemistry, radio frequency and physics. The principle of the propagation of distributions is extended to complex-valued quantities and the calibration process. All results of this work are integrated into the software project MUSE. Therefore, it is possible to apply the derived results in practice.