The concept of a More Electric Aircraft (MEA) demands a highly optimized airframe power system which is achieved by replacing pneumatic and hydraulic systems with energy efficient electrical systems. With increasing power offtake requirements, the More Electric Engine (MEE) could play a key role in future MEA, where more electrical power will be drawn from gas turbine shaft using the conventional gear driven electrical machine, which is known to present inefficiencies and reliability issues. Embedding an electrical machine directly at the engine shaft would help eliminate the need for the accessory gearbox along with potentially improving the reliability and efficiency of the whole system. However embedding the electrical machine presents significant design challenges to meet the key requirements. Some of these include: the necessity of the electrical machine to operate in high temperatures and high vibration environments, the mechanical constraints such as space limitations, and the need to operate at high speeds. Other requirements include the need for high power density, high torque density, high efficiency and maintenance-free operation of the electrical machines. At present, different electrical machine topologies have been developed for a number of challenging industrial and automotive applications where some of the requirements and criteria have been partially met. In this paper the detailed investigation and the trade study carried out of the various electrical machine topologies to understand their advantages, constraints and drawbacks is presented to provide a preliminary evaluation of their suitability for meeting the stringent requirements of embedded machines in aerospace applications.