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Light weight, high speed, compact power transmission shafts transmit torque through diaphragm type flexible discs whose planes are normal to the torque axis. The angular and axial misalignments are obtained by material flexure of these thin diaphragms within elastic limits. These shafts have multiple diaphragms used in series so that each diaphragm shares a portion of the total misalignment. Such shafts are used in high speed aircraft coupling engine mounted accessory gear box and aircraft mounted accessory gearbox. This paper deals with the design and development of light weight flexible power transmission shaft for high speed fighter aircraft application keeping critical speeds and weight as the design criteria. Since the number of design constraints is more, finite element analysis has been used as an effective tool for trying out various design iterations so that all the design constraints are met.