The use of virtually resistance-free superconducting windings in electrical machines is very attractive, since it offers the prospect of greatly reduced losses. The application of High Temperature Superconductors (HTS) greatly increases the economic appeal of these devices, since the cooling systems are simpler, and therefore cheaper and more reliable, than those required for low-temperature superconductors. Constant advances in superconductor technology have made it possible to obtain high-temperature superconducting tapes with increasing critical currents in lengths suitable for building electrical machines. These current densities are now much higher than those that can be used in a conventional winding; we expect to obtain a current density in excess of 50 A/mm2, whereas it is difficult to cool a copper winding if the current density exceeds 10 A/mm2. The E-J characteristic of superconductors is highly non-linear; if the current density is significantly below the critical current density, the electric field is negligible. In addition, the critical current is reduced in the presence of high B fields. For the HTS material used, this field dependence is highly anisotropic; the component of B normal to the face of the tape has a much greater effect than the other components. The much higher current density may allow the output power of the machine to be increased or its size and mass to be reduced. Alternatively, it may be used to allow a machine to be built with no rotor core, thereby reducing the mass of the machine and, in particular, that of the rotor. For the current project, we intend to build and test a synchronous generator with a high-temperature superconducting coreless rotor. A number of different design concepts have been considered. For each, some limited optimisation of the electromagnetic performance has been done using a commercially available finite element (FE) package. In all the designs considered, magnetic flux diverters are used to reduce the values of B in the superconducting coils. The FE models were also used to confirm that the B field in the coils is consistent with the expected current. In addition, structural finite-element models were built in an attempt to prove that a satisfactory design could be produced. The structural design of a superconducting rotor is not straightforward. There are two principle conflicts that account for this difficulty. The structure that supports the cold rotor components must limit the heat load that it imposes on the cooling system, while being sufficiently stiff to keep the critical speeds of the rotor out of the working range. The structure must be strong enough to carry the loads imposed by centrifugal force, while being flexible enough to adsorb differential thermal contraction without generating excessive stress. This process will allow identifying the challenges of building that type of machines and suggesting possible solutions to problems that the future designers of similar devices might face. The project combines a number of the EPE group interest fields: finite element modelling, optimisation, superconductivity and electrical machines.