Transient mathematical models are presented for an active single basin solar still (ASS) with and without a sensible storage material under the basin liner of the still. Sand is used as a storage material due to its availability. The flowing water temperature is assumed to vary with time and space coordinates. Analytical expressions are obtained for various temperatures of the still elements as well as for the temperature of sand. The performance of the still with and without storage is investigated by computer simulation using the climatic conditions of Jeddah (lat. 21 degrees 42' N, long. 39 degrees 11' E), Saudi Arabia. Effects of mass flow rate and thickness of the flowing water for different masses of the storage material on the daylight P-dl, overnight P-on and daily productivity P-d and efficiency eta(d) of the still are studied. The dependence of P-d and eta(d) on the thickness and thermal conductivity of the basin liner material is also investigated. It is found that P-d and eta(d) decrease as the mass of the storage material increases, due to the increased heat capacity of the storage material. Furthermore, P-d and eta(d) are found to decrease with increasing thermal conductivity of the basin linear material. Therefore, it is advisable to fabricate basin liners of ASS from cheap insulating materials such as glass and mica with an optimum thickness of 3 mm. On a summer day, a value of P-d of 4.005 (kg/m(2) day) with a daily efficiency of 37.8% has been obtained using 10 kg of sand compared to 2.852 (kg/m(2) day) with a daily efficiency of 27% when the still is used without storage. The annual average of daily productivity of the still with storage is found to be 23.8% higher than that when it is used without storage. (C) 2009 Elsevier B.V. All rights reserved.