Copper biosorption by Arthrobacter sp. has been studied in this work. The process has been realized inside of a ultrafiltration/microfiltration (UF/MF) reactor in order to confine cells. A mathematical model has been developed that is able to predict experimental data under different operating conditions. The model takes into account different phenomena, which might occur during the process, such as a dependence of equilibrium parameters on pH, a partial cell disruption, and a change in the membrane retention properties at high biomass concentrations. Experimental tests have been performed under different operating conditions: a full factorial design has been implemented with pH (levels: 4, 5, and 6 units) and biomass concentration (levels: 1 and 5 g/L) as factors. A simple mathematical model based on metal mass balance taking into account the effect of pH on the Langmuir equilibrium adsorption parameters well fitted experimental data at low pH values and biomass concentrations. A more complex mathematical model, which considers a partial cell disruption during the biosorption trial, was proposed to understand and analyze the anomalous system behavior at pH = 6 and biomass concentration equal to 5 g/L. The effect of mechanical stress on biomass performances was also examined by using a discontinuous system (test tube trials) simulating the membrane reactor apparatus. In this alternative system biosorption trials were carried out in test tubes in such a way to avoid or at least minimize the disruption due to mechanical stress. Experimental results obtained by using this system can be modeled up to pH = 5 without considering cell disruption phenomenon, while at pH = 6 possible chemical reactions of biomass constituents could happen.