A heat driven thermoacoustic cooler consists of a thermoacoustic engine that converts heat into acoustic waves, coupled to a thermoacoustic cooler that converts this acoustic energy into cooling effect. These machines have simple structures without moving parts. The coupling of a solar concentrator and a heat driven thermoacoustic cooler seems to be an interesting alternative to the electrically driven compression vapour cycle. As the other solar refrigeration systems, even if the cooling demand generally increases with the intensity of the solar radiation, one of the major difficulties is to insure a frigorific power supply when there is no or low solar radiation. In our prototype, in order to guarantee a sufficient cooling capacity to face to refrigeration loads in spite of the production fluctuations, a latent cold storage has been considered. The aim of the work presented here is to investigate the behaviour of this key element under several design and operative conditions. A description of the future prototype is done insisting on the thermoacoustic refrigeration and the cold storage system. A modelling of the main elements of the prototype is developed. The results of simulations under real solar radiation as well as a parametric study considering the main design and operative parameters of the cold thermal storage system are presented.