The shear viscosity and normal stress difference of two filled and two unfilled thermotropic liquid crystal polymer (TLCPs) were studied. The rigid and rod like molecules of TLCPs orientate differently at different shear rates. Under low shear rate, the molecules tend to align in the direction of the flow but also tumble and wagging on their own axis. The abnormal orientation of the molecules also depends upon temperature, fillers contents, aspect ratio and elastic nature of LCP molecules. These behaviors lead to unusual theological properties of LCPs, such as negative first normal stress difference for filled LCPs at low shear rates. But with the increase of shear rate, the molecules are oriented in the direction of flow, which lead to isotropic flow at high shear rates. The complicated rheological properties and characteristic anisotropic properties of LCPs are modelled by recently developed Leonov's viscoselastic constitutive equations. Simulation has been carried out using Mathematica software and the characteristic anisotropic properties of LCPs have been identified. The experimentally measured viscosities at high shear rate have been compared with model predictions. Moreover, the normal stress differences using at high shear rates have been estimated using Leonov's model, which is experimentally not accessible.