Recently, Low Power Wide Area Networks (LPWANs) have attracted a great interest due to the need of connecting more and more devices to the so-called Internet of Things (IoT). LoRa networks are LPWANs that allow a long-range radio connection of multiple devices operating in non-licensed bands. In this work, we characterize the performance of LoRa's Uplink communications where both physical layer (PHY) and medium access control (MAC) are taken into account. By admitting a uniform spatial distribution of the devices, we characterize the performance of the PHY-layer through the probability of successful decoding multiple frames that were transmitted with the same spreading factor and at the same time. The MAC performance is evaluated by admitting that the inter-arrival time of the frames generated by each LoRa device is exponentially distributed. A typical LoRaWAN operating scenario is considered, where the transmissions of LoRa Class A devices are affected by path-loss, shadowing and Rayleigh fading. Numerical results obtained with the modeling methodology are compared with simulation results, and the validation of the proposed model is discussed for different levels of traffic load and PHY-layer conditions. Due to the possibility of capturing multiple frames simultaneously, we consider the maximum achievable performance of the PHY/MAC LoRa scheme according to the Signal-to-interference-plus-noise ratio (SINR). The contribution of this work is primarily focused on studying the average number of successfully received LoRa frames, which establishes a performance upper bound due to the optimal capture condition considered in the PHY-layer.