We consider a relay network based on Unmanned Aerial Vehicles (UAV). Terrestrial Base Stations (TBS) and UAV Relay Nodes (RN) are modelled using two Homogeneous Poisson Point Processes (HPPP). UAVs can hover at a fixed position or move following specific displacement schemes. The Coverage Probability (CP) of a typical user equipment (UE) is derived, either when it communicates via a direct link (from the TBS to the UE) or via a relay link (from the TBS to the UE through a UAV RN). Every link can be in Line-of-Sight (LoS) or Non Line-of-Sight (NLoS), and suffers from Rician fading with distance-dependent parameters. This coverage is calculated by means of both stochastic geometry (SG) and Monte-Carlo (MC) simulations. The benefits of the use of UAV as RNs are analysed depending on their altitude, density, and mobility scheme.