In this paper, exact signal-to-interference-plus-noise ratio (SINR) analysis of direct-sequence ultra-wideband (UWB) systems with rake receiving in the presence of inter-symbol interference and multiple-access interference over realistic UWB channel models is conducted. The SINR expression, considering the code correlation functions and a generic rake receiver with variable number of combining fingers, is first derived. The statistics of the UWB channel models, defined by the IEEE 802.15.3a Task Group, are then taken into account. Because of the high multipath resolution offered by UWB signals, the UWB channel exhibits a unique path-arriving phenomenon, which can, however, complicate the analysis. Nevertheless, by exploiting the property of Poisson path arrivals, the exact average SINR is obtained in this paper. The analytical results well match computer simulations and can readily be applied to the performance evaluation or system optimization over realistic channel and interference models.