The influence of cross-flow velocity and transmembrane pressure on the optimal back-shock frequency and normalized net flux during back-shocking has been studied using a semi-analytical mathematical model. The model uses the flux as a function of time without back-shocking together with knowledge of the streamlines and pathlines during the back-shock cycle to predict the optimal normalized net flux as a function of forward filtration time. The model was used to investigate three different transmembrane pressures and three different cross-flow velocities during a back-shock cycle. The net flux was found to increase under all operating conditions when using back-shocking. The greatest increase in normalized net flux was found at the highest cross-flow velocity and the highest transmembrane pressure, and corresponds to an increase of 37% compared to the steady-state flux. The highest cross-flow velocity and the highest transmembrane pressure gave the highest optimal back-shock frequency of 0.21 Hz. The optimal back-shock frequency was found to decrease with increasing pressure and decreasing cross-flow velocity. The model is easy to use in different applications as it is easy to measure flux during forward filtration without back-shocking. Good agreement was found between the semi-analytical model and a model based on computer fluid dynamics in predicting both the value of the optimal normalized net flux and the optimal back-shock frequency. (C) 2016 Elsevier B.V. All rights reserved.