It is common practice to model the base station (BS) locations in a cellular system by a grid, such as a hexagonal or square lattice. This model is usually analytically intractable as well as quite idealized. Therefore, system designers resort to complex simulations to evaluate network performance. In this paper, we introduce a new model for the base station locations based on a homogeneous Poisson point process (PPP), whereby the mobiles communicate with their nearest base stations. We obtain the distribution of the signal-to-interference-noise ratio (SINR), compute the average ergodic rate, and analytically verify the trade-off between coverage and rate with frequency reuse. We compare our results with actual BS locations as well as the grid model. In addition to being tractable, we also observe that the performance predicted by the PPP model lower bounds the actual performance, and is about as predictive as the grid model which provides upper bounds