This paper presents a new framework for analyzing downlink cellular networks using stochastic geometry, which is more tractable than traditional grid-based models. The authors develop general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) and derive expressions for the downlink SINR cumulative distribution function (CCDF) and mean rate. These expressions involve computable integrals and can be simplified to common integrals or closed-form expressions in special cases. The coverage probability is derived for various scenarios, including exponentially distributed interference power, path loss exponent of 4, and interference-limited networks. The proposed model is compared with traditional grid-based simulations and actual base station deployments, showing that it provides a reliable lower bound on coverage while the grid model provides an upper bound. The paper also explores the impact of frequency reuse on coverage and rate, finding that increasing frequency reuse improves coverage but decreases the overall sum rate. The proposed model is more accurate and tractable, especially for future networks with opportunistic and dense base station placements.This paper presents a new framework for analyzing downlink cellular networks using stochastic geometry, which is more tractable than traditional grid-based models. The authors develop general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) and derive expressions for the downlink SINR cumulative distribution function (CCDF) and mean rate. These expressions involve computable integrals and can be simplified to common integrals or closed-form expressions in special cases. The coverage probability is derived for various scenarios, including exponentially distributed interference power, path loss exponent of 4, and interference-limited networks. The proposed model is compared with traditional grid-based simulations and actual base station deployments, showing that it provides a reliable lower bound on coverage while the grid model provides an upper bound. The paper also explores the impact of frequency reuse on coverage and rate, finding that increasing frequency reuse improves coverage but decreases the overall sum rate. The proposed model is more accurate and tractable, especially for future networks with opportunistic and dense base station placements.