Losses in bus bars carrying AC current and passing near the tank wall in transformers can contribute significantly to stray losses and can produce high temperatures on the tank wall. Usually these losses are mitigated by moving the bus bars farther away from the wall or by placing a shield of high conductivity and low permeability on the tank wall near the bus bars. Although these losses in the wall or shield can be calculated by modern finite-element codes, an analytical method would obtain these losses quickly during the design phase. We present such a method here. The method works for an arbitrary collection of bus bars carrying currents from different phases. Applications to other situations where long cables or bus bars carrying AC currents and running parallel to a conducting plate are also possible.