An LED lamp uses a flexible metal fabric as a heat sink. At least one light emitting diode is attached to a circuit board that is mounted on a heat conducting member. The flexible heat sink is attached to the heat conducting member, such that heat generated by the light emitting diode and circuit board is conducted to the flexible heat sink. The flexible heat sink can be deformed to fit in a variety of spaces. The flexible heat sink dissipates the heat generated by the LED lamp without the need for a fan. The flexible heat sink may be made from braided copper fabric.