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Magnet coils are investigated which can produce magnetic fields of 15–40 MA/m (200–500 kOe) during working times of the order of 0.1 sec. These fields are suited for measurements in highly conducting materials. The coils are precooled to 20°K or 77°K and the Joule heat is not removed during the pulse. In Sec. I the thermal limitations of this method are reviewed. Plots are given for the optimum dimensions and current densities for coils producing a specified field during a specified time, minimizing the necessary power supply. Details of a magnet constructed along these lines are given. The maximum field produced by this coil, 16 MA/m (200 kOe) during 0.3 sec, however, proved to be determined by mechanical instabilities. These problems are reviewed in Sec. II. Calculations of the Lorentz force and the internal stresses resulting from it were carried out taking the elastic and plastic properties of copper and insulation into account. It is shown theoretically that a magnet stable to 35 MA/m (440 kOe) can be built from hard drawn copper if a reinforcing steel cylinder is used at a certain radius inside the coil.