The performance of a multidisciplinary system is ineluctably affected by various sources of uncertainties, which are often categorized as aleatory (e.g. input variability) or epistemic (e.g. model uncertainty) uncertainty. Statistical sensitivity analysis (SSA) exists in literature for studying the impact of different sources of uncertainties on system performances. However, epistemic uncertainty, as an important source of uncertainty, is seldom taken into consideration. Applying SSA for a multidisciplinary system is even more challenging due to the complexity in system analysis as well as the coupling relationship between subsystems. In this research, we develop a multidisciplinary statistical sensitivity analysis (MSSA) approach to analyze the contributions from various sources of uncertainties. Both global and local sensitivity analyses are conducted; the former studies the impact of variations over the entire range of model inputs, and the latter compares the impacts of aleatory and epistemic uncertainties to facilitate decision making in further data collection for reducing system uncertainty. Two types of sensitivity metrics are proposed for MSSA: the extension of the traditional variance-based sensitivity indices, and the relative-entropy-based sensitivity indices for the situation with irregular system performance distribution. To overcome the computational challenges in MSSA, we establish a mathematical approach, i.e. multidisciplinary uncertainty analysis (MUA), for handling the complexity because of the coupling relation among multiple disciplines and propagating uncertainty across multiple levels (component/subsystem/system). An aircraft design problem consisting of three coupled disciplines is used to demonstrate the effectiveness of the proposed MUA method and MSSA approaches.