Highly flexible superconducting Ag/Bi-Pb-Sr-Ca-Cu-O wires have been fabricated by the powder-in-tube technique. The J(c) remains unchanged when wires of superconductor thickness 25-mu-m are bent to a radius of curvature as small as 4 mm up to 10 times. This flexibility is of technological importance since tapes can be wound into coils, a form suitable for many applications, without need for further heat treatment. This also simplifies the handling, storage, and installation. The J(c) has been measured to have values up to 19,000 A/cm2 at 77 K and zero field, 14,000 A/cm2 at 77 K and 0.1 T, and 6,200 A/cm2 at 77 K and 1.0 T for tapes with a cross sectional area of 0.126 mm2. A combination of the grain alignment, intimate contact between grains, and high density of defects is believed to be responsible for the improvement in the J(c)-H characteristics.