A CICC type superconducting bus-line electrically connecting a superconducting magnet to a power supply is cooled down to low temperature under the external magnetic field during operation. The thermal contraction during the cooling may be constrained by the supports which are installed to protect the bus-line from Lorenz magnetic forces. This constrained contraction causes thermal stresses in the bus-line to release thermal contraction. The minimum stress conditions in the bus-line may be optimized by controlling the supporting arrangement considering the thermal contraction and the external field. The analytical method to find optimal supports arrangement was suggested by using the beam theory, and numerical calculation using commercial code was performed to verify the suggested analytical optimization method.