When a material volume consisting of an uncured rubber matrix reinforced with two non-parallel sets of embedded reinforcement wires or cords is subjected to large deformations, pantographing may occur. In other words, the angles between reinforcement wires change. We introduce a simple phenomenological fluid model suitable for the numerical prediction of pantographing, as can be encountered in industrial processes such as the manufacturing of rubber tires or reinforced hoses. The reinforced material is described with an orthotropic continuous fluid model. Here the reinforcement wires or cords are accounted for by the orthotropy, whose direction is locally affected by the deformation undergone by the matrix, and is updated accordingly. The model is subsequently applied to the simulation of a sagging experiment, where the role of pantographing is illustrated.