There are still areas around the world suffer from severe shortage of freshwater supplies. Desalination technologies are not widely used due to their high energy usage, cost, and environmental damaging effects. In this study, a mathematical model of single-bed adsorption desalination system using silica gel-water as working pair is developed and validated via earlier experiments. A very good match between the model predictions and the experimental results is recorded. The objective is to reveal the factors affecting the productivity of fresh water and cooling effect in the solar adsorption system. The proposed model is setup for solving within the commercially-available software (Engineering Equation Solver). It is implemented to solve the mass and heat balance equations for the adsorbent bed, condenser, and evaporator components. At a typical temperature of 89 °C and flow rate of 30 m3/sec for the hot water entering the bed, the following results are reported: (a) the specific daily water production of 1.89 m3 /ton of silica gel/ day, (b) coefficient of performance of 0.32, and (c) specific cooling power of 40.82 W/kg of silica gel. The concentration of salt (X) in the product (desalinated water) has been set with value of 0.5 gm/kg to be suitable for drinking and irrigation. The salt concentration in the evaporator is estimated to be 4.611 gm/kg during the overall adsorption process. The results from this study should be of wide interest for the field of solar water desalination and air-conditioning.