The interest of the scientific and industrial communities on the application of high altitude stratospheric platforms to communications is increasingly growing. Several research projects and field trials are being carried out by international consortia and specific portions of the electromagnetic spectrum have been allocated by the International Telecommunications Union (ITU) for communications applications. The channel experienced by such systems plays a key role for the provision of reliable communications services but, unfortunately, its inherent characteristics are substantially different from those of other channel typologies. Therefore, in order to design and simulate effective propagation impairment mitigation techniques such as adaptive modulation and coding or adaptive beamforming and equalization algorithms, an ad hoc channel model and simulator is definitively required. In this paper a novel channel model and a related channel simulator especially tailored for HAP-based communication systems are presented. The model is conceived for link-level simulations of point-to-point communication links, wherein both the transmitter and the receiver may be equipped with an array of antennas. Peculiar physical effects of the stratospheric channel are taken into account as well as impairments due to the possible presence of scatterers and relative movement of both transmitting and receiving stations. The structure of the channel simulator has been conceived to maintain the computational burden at required by the channel simulator is kept low by an efficient tapped delay line implementation.