A simple numerical model that describes the altitude effect of solar UV flux under cloud-free conditions was developed and tested. The model computes the direct and diffuse UV irradiances for the wavelength range 290-385 nm, at any sub-polar location and time (restricted to arid areas). The input parameters include extraterrestrial solar irradiance, ozone content and vertical distribution, aerosol amounts and size distribution, SO2 and NO2 contents, surface albedo and solar zenith angle. Model results were compared with measurements made in the tropical Chilean Andes for altitudes up to 5500 m above sea level. The model and data show good agreement. For the measured direct component a linear increase with altitude was assumed, whereas model results, computed up to 15 km altitude, exhibit a non-linear behavior. However, in the lowest few kilometers a linear regression was adequate for both model and measurements. As for the diffuse component, the variation with altitude strongly depends on wavelength and solar zenith angle. At short wavelengths and large solar zenith angles, a pronounced maximum occurs at a level which depends on these parameters. The maximum cannot be observed when integrating;over the UV-A range. This behavior can be understood by taking into account the sources of the diffuse flux at any given level in the atmosphere.