A novel design of coils for transcutaneous magnetic stimulation of nerves is presented. These coils consist of a toroidal winding around a high-permeability material (Supermendur) core embedded in a conducting medium. Theoretical numerical calculations are used to analyze the effect of the design parameters of these coils, such as coil width, toroidal radius, conducting layer thickness and core transversal shape on the induced electric fields in terms of the electric field strength and distribution. Results indicate that stimulation of nerves with these coils has some of the advantages of both electrical and magnetic stimulation. These coils can produce localized and efficient stimulation of nerves with induced electric fields parallel and perpendicular to the skin similar to surface electrical stimulation. However, they retain some of the advantages of magnetic stimulation such as no risk of tissue damage due to electrochemical reactions at the electrode interface and less uncomfortable sensations or pain. The driving current is reduced by over three orders of magnitude compared to traditional magnetic stimulation, eliminating the problem of coil heating and allowing for long duration and high-frequency magnetic stimulation with inexpensive stimulators.