This paper investigates autonomous dynamic soaring maneuvers for a small Unmanned Aerial Vehicle (sUAV) having the capability to morph. Dynamic soaring for UAVs have mostly been confined in literature to fixed configurations. In order to analyze the extent to which dynamic soaring is influenced by different morphologies, an innovative concept of integrating dynamic soaring with morphing capabilities is introduced. Moreover, optimal soaring trajectories are generated for two basic wing morphologies: variable sweep and variable span. Three-dimensional point-mass UAV equations of motion and nonlinear wind gradient profile are used to model the flight dynamics. Parametric characterization of the key performance parameters is performed to determine the optimal platform configuration during various phases of the maneuver. Results presented in this paper indicate 15% lesser required wind shear by the proposed span morphology and 14% lesser required wind shear by the proposed sweep morphology, in comparison to their respective fixed wing counterparts. This shows that the morphing UAV can perform dynamic soaring in an environment, where fixed configuration UAVs might not, because of lesser available wind shears. Apart from this, span morphology reduced drag by 15%, lift requirement by 11% and angle of attack requirement by 20%, whereas increased the maximum velocity by 6.2%, normalized energies by 9% and improved loitering parameters (approximately 10%), in comparison to fixed span configurations. Similarly, sweep morphology guaranteed 20% drag reduction, 16% lesser angle of attack requirement and improved loitering performance over the fixed sweep configurations. The results achieved from this study strongly support the idea of integrating dynamic soaring with morphing capabilities and its potential benefits.