A quantitative model is presented for the high critical current densities (J c ) supported by superconducting materials with uniaxial alignment, such as c-axis textured Bi-Sr-Ca-Cu-O tapes. Current follows percolative paths across small-angle grain boundaries. Because j c is low for intragranular conduction parallel to the c axis, the 3D flow required for percolation is produced by conduction perpendicular to the c axis in tilted grains. For optimized microstructures, J c ranging from 3 to 30 % of the intragranular value is predicted for percolation across small-angle grain boundaries with misorientations below 10°and 20°, respectively.