Albatrosses use a flight manoeuvre which is called the dynamic soaring, to gain energy from horizontal wind gradient so as to travel for a very long journey and the period almost goes on without making stopovers or flapping their wings. Dynamic soaring is considered a promising technique which can be widely applied to UAV (unmanned aerial vehicle) for extending mission capabilities. The EOM (equation of motion) of a small UAV in the gradient wind field was derived and simplified in the airpath frame of axes based on the flight dynamics. According to the theorem of kinetic energy and mechanical energy variation with respect to the noninertial frame of reference respectively, the energygain mechanism during dynamic soaring was analyzed by using the simplified EOM. The differential flatness method was employed to solve loiter pattern and travel pattern trajectories for the objective function of minimum average change rate of control inputs. The analysis result indicates that the upwind climb and downwind dive is the basic energygain ways of dynamic soaring. The optimal results show that the control inputs are smoothed，even the staged constant inputs to make the actual control simpler. In the optimization of loiter pattern，when the wind gradient is treated as a decision variable, the optimization process finds the optimal wind gradient in the range of ［0，0.5 s^-1］ for the objective function. While in the optimization of travel pattern, the value of the objective function is monotonically decreasing in the same range. 