A method of forming a textured superconductor wire includes constraining an elongated superconductor precursor between two constraining elongated members placed in contact therewith on opposite sides of the superconductor precursor, and passing the superconductor precursor with the two constraining members through flat rolls to form the textured superconductor wire. The method includes selecting desired cross-sectional shape and size constraining members to control the width of the formed superconductor wire. A textured superconductor wire formed by the method of the invention has regular-shaped, curved sides and is free of flashing. A rolling assembly for single-pass rolling of the elongated precursor superconductor includes two rolls, two constraining members, and a fixture for feeding the precursor superconductor and the constraining members between the rolls. In alternate embodiments of the invention, the rolls can have machined regions which will contact only the elongated constraining members and affect the lateral deformation and movement of those members during the rolling process.