In recent years, operators addressed the explosive growth of mobile data demand by densifying the cellular network so as to achieve a higher spectral efficiency and increase their capacity. The intense proliferation of wireless devices resulted in interference limited networks, which suggests the use of interference mitigation and coordination techniques. In this work, we study successive interference cancellation (SIC) for uplink communications and we define an analytical framework that describes the performance benefits of SIC which accounts for the computational complexity of the cancellation scheme and the relevant network related parameters such as the random position and density of the base stations and mobile users, and the characteristics of the propagation channel. In our analysis, we explicitly model the consecutive events of canceling interferers and we derive expressions of the success probability to cancel the kth strongest signal and to decode the signal of interest (SoI) after k cancellations. The analysis indicates that the performance benefit of SIC diminishes quickly with k. The framework also reveals that a substantial performance gain can only be obtained for low values of the target signal-to-interference ratio (SIR).