Ornithopters or flapping wing Unmanned Aerial Vehicles (UAVs) have potential applications in civil and military sectors. Amongst the UAVs, ornithopters have a unique ability to fly in low Reynolds number regions and also have the agility and maneuverability of a rotary wing aircraft. In nature, birds achieve such special characteristics by morphing their wings. The compliant spine (CS) design concept presented here represents a novel method of achieving wing morphing passively. In this paper, an optimal design method is developed that incorporates dynamic finite element analysis. To solve the CS design problem a new multi-objective optimization problem is formulated with three objective functions. The first objective function seeks to minimize the mass of the compliant spine. The second objective function seeks to maximize the deflection of the compliant spine for a particular dynamic loading condition. Finally, the third objective function seeks to minimize the stress in the design observed under the dynamic loading conditions experienced during flight. The deflections and stresses in the CS design are based on measured wing loads and are calculated by applying a sinusoidal forcing function at a prescribed forcing frequency. The optimization, performed via a controlled elitist genetic algorithm which is a variant of NSGA-II, is used to design CSs operating under dynamic conditions. Modal analysis and frequency response of an optimal compliant spine during the upstroke are also shown.