We present a formal model to represent and solve the unicast/multicast routing problem in networks withquality-of-service(QoS) requirements. To attain this, first we translate the network adapting it to a weighted graph (unicast) orand-orgraph (multicast), where the weight on a connector corresponds to the multidimensional cost of sending a packet on the related network link: each component of the weights vector represents a different QoS metric value (e.g., bandwidth). The second step consists in writing this graph as a program insoft-constraint logic programming(SCLP): the engine of this framework is then able to find the best paths/trees by optimizing their costs and solving the constraints imposed on them (e.g.delay≤ 40 ms), thus finding a solution to QoS routing problems.C-semiringstructures are a convenient tool to model QoS metrics. At last, we provide an implementation of the framework over scale-free networks and we suggest how the performance can be improved. The article highlights the expressivity of SCLP.