In this paper, we provide the model of the multi-layer aerial network (MAN), composed unmanned aerial vehicles (UAVs) that distributed in Poisson point process (PPP) with different transmission power, heights, and densities. In our model, we consider the line of sight (LoS) and non-line of sight (NLoS) channels, which is probabilistically formed. We first derive the probability distribution function (PDF) of the main link distance and the Laplace transform of interference of MAN by considering a transmitter/receiver association based on the strongest average received power. We then analyze the successful transmission probability (STP) of the MAN, and provide the upper bounds of the optimal UAV densities in each layer that maximize the STP of the MAN. Through the numerical results, we show the existence of the optimal height of the aerial network (AN) after exploring the performance tradeoff caused by the height. We also show both the optimal UAV density as well as its upper bound decrease with the height of the ANs.