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A new method is described for the design of gradient coils for magnetic resonance imaging systems. The method is based on the known equivalence between a magnetized volume surrounded by a conducting surface and its equivalent representation by a surface current density. The curl of a vertical magnetization vector of a magnetized thin volume is equivalent to a surface current density whose stream line defines a coil current pattern. This concept is applied to the design of gradient coils of arbitrary shape. The thin magnetized volume is discretized in small triangular elements. By calculating the contribution of each magnetized block at target points a field source matrix is obtained. The equivalent magnetization current concept is applied to obtain the equivalent coil impedance, force and torques. A quadratic programming optimization algorithm is used to obtain the stream-magnetization-thickness function value at each node such that coils of optimal performance are obtained. This method can be used for gradient coils wound on arbitrary surface shapes and can be applied to hybrid current/iron solutions. A variety of examples are shown to demonstrate the versatility of the method. A novel partially shielded 3-D biplanar gradient coil for open MRI magnets is presented.