Liquid Crystal Polymers (LCP) are high-performance polymers, which contain stiff, mostly rod-shaped molecular segments that are called mesogens. These mesogens are oriented when the melt is sheared or elongated. In this manner, a self-reinforcing effect is obtained which results in a higher elastic modulus and strength of the product. Unfortunately, these materials exhibit an untypical rheological behavior. LCP melts often show a flow curve with three regions. In this Paper, the rheological behavior of thermotropic LCP is studied using a high pressure capillary rheometer, which was equipped with a slit die. The pressure was measured at three positions along the die as well as before the entrance of the die. In some of the experiments the material seems to exhibit a power law behavior, which means that the viscosity curve is linear in the double logarithmic diagram. But the detailed analysis of all experimental investigations showed that the flow behavior cannot be described well with existing models. To deal with this issue, a new rheological model was developed. This new model combines the Bird-Carreau-Yasuda model with a specific yield stress parameter. In general, below such a yield stress a material does not flow . A Bingham fluid combines Newtonian behavior with a yield stress, a Herschel-Bulkley fluid combines a power-law behavior with a yield stress and this new model does the same with the Bird-Carreau-Yasuda approach. Analog to Bingham and Herschel-Bulkley only one additional parameter is needed. The temperature dependence of this yield stress is considered similar to that of the zero shear viscosity of the Bird-Carreau-Yasuda approach. The new model not only describes the determined data well but can also describe the three-region flow behavior observed by other authors excellently.