We introduce a simple phenomenological fluid model suitable for the numerical simulation of wire-reinforced polymers and rubber, as can be encountered in the industry. The reinforced system is described with an orthotropic continuous fluid model, where the orthotropy accounts for the reinforcement wires. The model is subsequently used for two simple applications. We first investigate the effect of reinforcement orientation on the sagging of a reinforced system. Next, we consider a more realistic situation of compression moulding for a stack of reinforced compounds.