With the increase of computing-intensive and delay-sensitive applications, mobile edge computing (MEC) technology has sprung up. It effectively satisfies the needs of user equipment (UE) for real-time computing resources by placing servers at the edge of the network. However, traditional MEC infrastructures are constrained by their fixed locations and emergency mobility needs. Unmanned aerial vehicles (UAVs) offer an effective solution with low cost, high mobility, and flexible deployment capabilities. In this paper, we propose a region-centric UAV-assisted MEC model, where the whole network space is divided into a set of hexagonal cells of equal area, and all UAVs in the same cell jointly process UE offloading data. Assume all UAVs are assumed to be equipped with independent MEC servers, and both UAVs and terrestrial UE follow independent homogeneous Poisson point process (PPP) distributions. Using the stochastic geometry analysis framework, we derive the successful uplink communication probability (SUCP) of uplink transmission for users. Finally, we compare the simulation results with the theoretical values to verify the model’s accuracy and evaluate the influence of key performance parameters on the network performance.