The aim of this paper was designing, dimensioning and mathematical modelling of a real absorption cooling device which uses binary mixture LiBr/water as working media. The studied device is installed as a part of the solar cooling plant in Dubrovnik in order to provide cooling for an office building of Vodovod Dubrovnik company. The energy needed for starting the absorption cooling process is provided through the solar field with total absorption area of 60 m^2. Besides that, 3 m^3 hot water tank and 1 m^3 chilled water tank are also embedded into the plant to reduct oscillations of Solar radiation and/or cooling capacity. In order to design and determine the dimensions of the device, a mathematical model was developed in ChemCAD software package and validated using an independent set of experimentally data from literature. After the validation, the model was used for the calculation of heat transfer area and coefficients of every process unit inside the device. This calculated data was then used during the MATLAB mathematical model development which was also validated and then used for determination of optimal working conditions of the device in order to achieve nominal cooling capacity of 17.5 kW. Sensitivity study was also done using the developed mathematical models. The results have shown that inlet temperatures of hot and cold utility streams have the main effect on the obtained cooling capacity and coefficient of performance of the system. Furthermore, it has also been found that temperature rise at the condenser and absorber outlet has negative effect on cooling capacity and coefficient of performance, while temperature rise at the evaporator outlet improves them. Besides that, higher temperature at the generator outlet and higher heat exchanger efficiency will also contribute to more efficient device operation.