The discovery of high-temperature superconductivity in rare- earth copper oxide ceramic systems has led to considerable research directed toward the development of electromagnetic components and devices. However, the application of high critical temperature superconductors has been limited because of crystal anisotropy of the randomly oriented grains in polycrystalline materials, grain boundary segregated phases and microcracking at the grain boundaries. These factors have resulted in low critical current densities and high residual resistivity. To address this problem, this research suggests laser-driven directional solidification of polycrystalline unsintered extrusions of high temperature superconducting materials under a controlled thermal gradient to produce highly anisotropic superconducting fibers having critical current densities. The innovation contained in this work is the use of laser heating to minimized phase segregation by heating very rapidly through the two-phase incongruent melt region. The technical objectives include developing a fiber extruder and a thermal gradient furnace, finding extruder operating conditions, evaluating laser melt parameters, fabricating and characterizing superconducting fibers and optimization of a proof-of-concept system. The significance of the laser driven direction solidification technique lies in the cost-effective production of high critical current density superconducting polycrystalline fibers.