A model for the shunt currents in an all-vanadium redox flow battery consisting of 3 stacks which are electrically connected in series. It is based on an equivalent circuit which treats the shunt current pathways as Ohmic resistors. The conductivity of the vanadium electrolyte has been measured for different state-of-charges in order to implement a dependency of the resistances on the state-of-charge of the system. Published results are used to validate the simulation data of a single stack. Three setups of pipe networks are evaluated using the model. The pipe connections between the stacks give rise to external shunt currents, which also increase the amount of shunt currents within the stacks. These connections also lead to a nonuniform distribution of the shunt currents. The effects of the shunt currents on the Coulombic efficiency and the energy efficiency of the system are studied by the means of the model.