A method of manufacturing a tubular woven hose cover includes feeding a plurality of longitudinal yarns into a weaving machine in an axial direction relative to the woven hose cover being made, weaving one or more radial yarns in and out of the plurality of longitudinal yarns in a radial direction relative to the woven hose cover being made, reducing a circumferential length of the one or more radial yarns and thereby generating a first cross-sectional diameter along a first portion of the woven hose cover, and increasing the circumferential length of the one or more radial yarns and thereby generating a second cross-sectional diameter along a second portion of the woven hose cover, wherein the first cross-sectional diameter is smaller than the second cross-sectional diameter.