The present work aims at studying the potentiometric response of an ion-selective electrode. The target material is a copper sulfide (CuS) thin film designed for the detection of Cu+2 ions in solutions. The electrode is prepared by mean of an electrochemical deposition of copper sulfide on a silicon substrate. The Cu+2 response is then studied and a near Nernstian behavior of this electrode is observed in the range of pCu 6-1. In order to quantitatively explain the exchange process behind the Cu+2 response, a stochastic computational method is established to explain the potentiometric response of the copper sulfide sensors that can be used for water pollutant detection. The numerical scheme is based on Monte Carlo simulation of ion exchange between the solution and the CuS membrane surface. The probability of this Cu+2 -ion exchange is implemented as the main factor, which governs the variation of the electrode potential vs. the Cu+2 concentration in the solution. Three characteristics of the detection response are studied, namely the detection threshold, the slope and the saturation concentration. The model validation is achieved by predicting the Nernstian behavior for the studied CuS sensor and by comparing the obtained results with data from the literature dealing with Cu+2 detection.