In modern times cardiovascular diseases (CVDs) constitute the major cause of death worldwide. Thus, improvements in diagnosis, treatment and prevention of CVDs could mean a further significant enhancement in global health care. In this context cardiovascular modelling plays a key role in order to gain valuable information on the human circulatory system. Especially a profound understanding of the pressure and flow waveforms of blood are of high interest since they reflect the physical state of a patient's arterial system. However, the mathematical models have to deal with considerably complex phenomena related to the wave propagation within the arterial tree. A very recent modelling approach meant to address this issue properly is called the Reservoir Theory. Several results have testified a promising ansatz of regarding the actual pressure waveform as an instantaneous sum consisting of an arterial compliance-related reservoir and a wave-associated excess pressure at the aortic root. Due to various experiments, it is believed that the same concept might suit for more distal locations too. Nonetheless, two assumptions are crucial to justify this extended reservoir concept: A similar pressure waveform decay at different arterial locations during diastole and a corresponding excess pressure proportional to the flow at the aortic root. In total 110 pairs of pressure and flow curves measured at the brachial and carotid artery were available in order to apply the Reservoir Theory on this data. Firstly, the reservoir concept was mathematically derived and theoretically investigated. In particular, two distinct " and practically important " methods were regarded: Method 1 is based on the knowledge of flow at the respective artery and method 2 relies on the extended reservoir concept which does not require the flow. Three different algorithms were used whereby two distinct computational approaches were considered for the latter method. Prior to the pressure separation, necessary data preprocessing was performed and its effects analysed. Moreover, the sensitivity of all algorithms to input parameters such as estimated notch time was pointed out. Based on these findings the respective algorithms got parametrized and, in further consequence, both the brachial and carotid pressure waveforms got separated. Their resulting reservoir curves were compared and systematic differences among all implementations discussed. Lastly, all computed reservoir waveforms and their deviated parameters were examined whereby a particular focus was put on clinically relevant indicators such as pulse pressure and area of pressure above diastolic blood pressure. The numerical results showed similar results of both algorithms associated with method 2. In contrast, remarkable differences with respect to both the reservoir pressures and their deviated parameters were witnessed as opposed to the first method. In the majority of cases, method 1 generated systematically higher pulse pressures and lower time constants indicating a steeper pressure decay in diastole. Furthermore, a notable sensitivity on the estimated notch time was observed among all implementations. Apart from that, the obtained reservoir curves differed for brachial and carotid data. In general, brachial reservoir curves exhibited lower figures in pulse pressure and area of pressure above diastolic blood pressure among both methods whereas total pulse pressure was slightly higher for brachial readings. Particularly, and with respect to method 2, the differences in pulse pressure and area of pressure above diastolic blood pressure between the corresponding brachial and carotid reservoir curves were, on average, about -4 mmHg and -2 mmHgs respectively. In contrast, the provided measured pressure waveforms exhibited mean figures of approximately +4 mmHg and -5 mmHgs for the respective differences after data preprocessing. Nevertheless, the second main assumption for the extended Reservoir Theory was, in case of its validity, mathematically refined. Overall, the findings suggest that the brachial and carotid reservoir curves do not meet the necessary assumptions to justify the application of the extended Reservoir Theory at these arterial locations. In particular, the assumed similarity of arterial reservoir curves is questionable. Thus, the pressure separation at the respective artery might rather be considered as a separation according to a local lumped parameter model. Moreover, the observed sensitivity to the estimated notch time of all algorithms causes doubts in terms of the reliable prediction of clinically relevant parameters.