A commercial high‐density polyethylene has been crystallized in the Instron Capillary Rheometer under the combined influence of pressure and orientation. A transparent high‐modulus, and highly oriented filament structure was produced. In order to determine quantitatively the degree of orientation, azimuthal x‐ray scans of the 002 reflection plane were used to obtain the orientation function of the orthorhombic unit cell relative to the flow axis in the rheometer (identified with the filament axis). A value of +0.996±0.002 was measured for this orientation function indicating that the backbones of the crystalline polyethylene chains were virtually aligned perfectly parallel to the flow axis of the rheometer. This report is concerned with the high‐resolution techniques required to measure such highly oriented samples. In conjunction with the x‐ray study, birefringence measurements are included which permit the determination of the orientation of the amorphous component as well as the crystalline component.