Conventional Magnetic Resonance Imaging (MRI) techniques require homogeneous main magnetic fields. However, MRI applications that are executed in inhomogenous main magnetic fields have been developed in recent years. In this study, RF coil geometries are designed for MRI applications in inhomogeneous magnetic fields. Method of moments is used to obtain the current density distribution on a predefined surface that can produce a desired magnetic field, which is perpendicular to the given inhomogenous main magnetic field. The basis functions are represented by Fourier series and a conductor pattern that can provide the calculated current density distribution is obtained using stream functions. The error percentages between the calculated and the desired magnetic fields are calculated and regularization techniques are used in order to obtain realizable conductor patterns. Taking the error and realizability of the conductor patterns into consideration, the optimum conductor patterns on cylindrical, cubic and planar surfaces are determined.