This paper presents a mathematical model of the weft yarn filling insertion process in rapier looms. A finite length segment of yarn is spatially discretized. Each element can interact only with the nearest neighbors by a viscoelastic interaction. The elastic and damping constants have been estimated by using experimental data obtained with different yarns. The resulting model has lumped parameters and it is completely described by a set of ordinary differential equations. The model provides the time and spatial profile of the tension in the considered yarn segment as a response to external forces applied to the weft yarn by the rapiers and the weft brake. Also, interactions with guide-eyes and piezoelectric feelers have been considered in the model. The simulation results confirm that the proposed model can be a useful tool in predicting weft yarn breakage and in design of tension control systems by weft braking action.