This work focused on the evaluation of the influence of incorporation of non-stationarity to the model of a batch circulating system for membrane-based extraction and stripping (BCSMES). Mass balance equations of the transferred component in a hollow-fibre (HF) contactor either for steady-state conditions or for unsteady-state conditions were derived. The mass balance of a HF contactor for steady-state conditions gives an ordinary differential equation. The mass balance of a HF contactor for unsteady-state conditions leads to a partial differential equation whose solution is generally considered to be more difficult than the solution of an ordinary differential equation. For the extraction loop of BCSMES and a system with a very high value of the distribution coefficient, D, the ordinary differential equation and partial differential equations were integrated. The analytical results were numerically compared with a solution of the system of 20 ordinary equations describing a cascade of 20 ideally mixed vessels and with selected experimental values.