We give numerically tractable, explicit integral expressions for the distribution of the signal-to-interference-and-noise-ratio (SINR) experienced by a typical user in the down-link channel from the k-th strongest bases stations of a cellular network modelled by Poisson point process on the plane. Our model comprises power-low path-loss model with arbitrarily distributed shadowing, with and without Rayleigh fading. Our results are valid in the whole domain of SINR, in particular for SINR<1, where one observes multiple coverage. In this latter aspect our paper complements previous studies reported in [Dhillon et al. JSAC 2012].