Provided is a storage tank or structure with conductive fiber material (e.g. carbon fiber) for dissipating electrostatic charge. The tank comprises a tank wall made of composite material, such as polyester-fiberglass composite. On an inner tank surface, open areas are provided in which the conductive fiber is exposed. The conductive fiber material has broken fiber tips and stray fibers for collecting electrostatic charge. Outside the open areas, the conductive fiber material is covered with a layer of cured resin. The conductive fiber is exposed only in the open areas. An impermeable film may be present under the conductive fiber in the open areas. The present invention also includes a method for making the tank, in which a liquid, gel, or impermeable film mask is applied to the conductive fiber material. The mask functions to prevent infiltration of liquid resin into the conductive fiber material.