Design possibilities of single and double Helmholtz coils of rectangular cross section have been investigated for the purpose of generating magnetic fields which have the same or even better uniformity as compared to that achieved with the idealized coils of negligible winding cross section. It is shown that the optimum dimensions of coil configuration can be determined by means of numerical analysis, even under such practical conditions that the ratio of thickness to width of winding cross section and the turn ratio of the coil pairs should be ratios of relatively small integers. It is also suggested that the balancing method provides a possible means of extending the uniform region one and a half times as much as that achieved with the idealized coils of negligible winding cross section.