A new and simple approach for modelling solute transport in fractured rock is presented, based on our previously used Channel Network Model (CNM). In our underlying concept, solute transport in fractured rocks takes place through undulating flat channels in the rock fractures. The channels form a 3-dimensional network. For non-interacting solutes the volume of the channels determines the residence time of a stream of water. For sorbing radionuclides the residence time is mainly determined by the ratio between the Flow Wetted Surface (FWS) and the flow rate in the channel (Q), in addition to the parameters that determine the interaction between the rock and the radionuclides. The main question explored in this paper is whether it is necessary to solve the flow problem for each studied case. From previous investigations, we have found that the flow rates in the channels where the solutes travel are closely related to the transmissivities of the channels. Simulations are presented in which streams of water are allowed to randomly select channels and trace out the paths where the path volume and its FWS can be assessed. The results obtained in this manner for the RTD (Residence Time Distribution) show rather good agreement with those obtained by solving the full flow problem and tracing particles in the network.