In this paper, the uplink (UL) signal-to-interference ratio (SIR) distributions in a two-tier heterogeneous cellular network (HCN) are analyzed by considering the power control effect and approximating the UL interferer locations as a non-uniform Poisson point process (PPP). Approximated closed-form SIR distributions are provided according to the tier, association rule, power control strategy for each tier, and resource partition (common or dedicated) and are shown to be quite close to the true distributions in a wide range of network parameters.