We propose a novel coupling algorithm, based on the operator-splitting scheme, which implements the viscoelastic wall law at the coupling nodes of the vessels. Two different viscoelastic models are used (V1 and V2), leading to five different computational setups: elastic wall law, model V1 applied at interior and coupling grid points, model V1 applied only at the interior grid points (V1-int), model V2 applied at interior and coupling grid points, model V2 applied only at the interior grid points (V2-int). These have been tested with two arterial configurations: (i) single artery, and (ii) complete arterial tree. Models V1-int and V2-int lead to incorrect conclusions and to errors which can be of the same order as, and are at least 1/5 of, the difference between the results with the elastic and the viscoelastic laws. Both test cases demonstrate the importance of modeling the viscous component of the pressure-area relationship at all grid points, including the coupling points between vessels or at the inlet/outlet of the model.