To provide detailed and accurate electric fields in the ion source-puller region and at the dee dummy-dee gap for a cyclotron, a relaxation method solution of Laplace's equation has been used. A conventional difference equation with variation in mesh size and relaxation factor as well as different schemes for boundary corrections have been developed to achieve roughly 1 percent accuracy for a thre-dimensional domain with 10/sup 6/ mesh points. Although the computation requires considerable computer time, it is much less expensive than electrolytic tank analogue methods for measuring field distributions around complex electrode configurations.