The number of industrial applications has increased exponentially in the last decades and the need for effective water treatment methods has become more essential as demand for pure water has increased. It is no longer possible to fulfil the rapidly growing demand worldwide using natural water resources. Low pressure membrane filtration with inside-out dead-end driven UF-/ MF- capillary membranes has been widely inserted in water and wastewater treatment plants to remove colloids and suspended particulate matter. However, the implementation of this technology has been limited by several factors. These include concentration polarisation, membrane fouling and particles which remain inside the capillary after backwashing. An efficient backwash process is a determining factor in ensuring effective membrane filtration and enhance the separation of the particles in the capillary membrane. By optimising the backwash process, hydraulical irreversible membrane fouling can be minimised and membrane permeability recovered, and the operating costs of the filtration process can consequently be controlled. In the context of this thesis, a numerical approach to the detailed description of the fluid dynamics process in capillary membrane during backwashing is developed and partially validated by experiments. Moreover, the study contributes to a better understanding of the conditions for potential formation of agglomerates inside the capillary, which lead to increased operating pressure during the process and may clog the capillary. The presented model investigates a variety of parameters associated with the backwash process in dead-end capillary membrane, such as operation parameters, in particular the operating pressure as a function of time, particle properties (size and density) and initial particle distribution in addition to capillary arrangement (vertical/horizontal). The evaluation of these data concentrates on observation and analysis of particle behaviour and distribution in a cross-sectional plane and along the capillary length. Based on the fluid flow and particle distribution, the eventual formation of particle plugs inside the capillary membrane is predicted. For this purpose, a multiphase flow model was developed to describe the fluid flow and particle motion inside the capillary membrane. The numerical model considers the interaction between the involved phases in terms of lift, virtual mass and drag forces. The simulations are carried out using different configurations of the initial particle distribution, homogeneous distribution, evenly and unevenly deposited particles. The model is coupled with a population balance equation to account for particle agglomeration and breakage. Furthermore, the pressure drop as well as the shear stress on the membrane surface inside the capillary during the backwash process are estimated. Based on the fact that during the backwash there are tightly adhered layers which cannot be removed, the influence of these layers on the process is taken into account. The simulation results show a good agreement with the experimental data in terms of the flow rate during the backwash process and particle removal at certain operating pressures.