Constantly increasing demand for electrical power requires more efficient and more powerful machines to be built. The conventional technology cannot provide such machines. It cannot deliver machines that are smaller, lighter and provide larger torques and power ratings. The answer to these problems is believed to be in superconducting machines. After short introduction to the phenomena of superconductivity and superconducting devices, practical superconducting tapes are described. The evolution and problems considered during the design of a coreless superconducting rotor for a synchronous machine are described. A few possible coreless rotor configurations are characterised and a simple formula is used to minimise the harmonic content. Estimation of machine parameters and evaluation of losses is also conducted. The areas to which particular attention has to be paid are pointed out. All these are undertaken for a demonstrator size machine with BSCCO windings. But to achieve real benefits it is important to build a machine that more closely represents real machines. Hence an optimisation method is used to investigate the possibility of increasing the size of the machine.