In this work we present a novel Dual-Scale Skeleton model (DSS) to simulate the mesoscopic dual-scale flow inside a fibrous layup at an affordable computational cost. Instead of using a traditional Stokes-Brinkman model to govern the flow inside and around the tows, the flow domain is separated into three interconnected subdomains. For each subdomain, the three-dimensional mesoscale geometry of yarns and channels is replaced by their medial axis representation, on which the flow is simulated by FE method. The generation of a Hybrid Skeleton mesh (2D and 1D elements) allows to reduce the computational cost of the problem while still accounting for three-dimensional effects in the flow. This allows one to carry out mesoscale simulations on relatively large domains. Although further refinements are desirable, the DSS model shows potential for application in composites process modeling.