For a spacecraft to make scientific measurements in the upper atmosphere, it might be necessary for the spacecraft to "dip" into the upper atmosphere. This aeroassist maneuver presents stability challenges that are compounded if the spacecraft contains long flexible booms. Several stability aspects that are unique to this flexible class of spacecraft undertaking an aeroassist are examined. Using a detailed, linear model, simple analytic equations are developed to predict the stability of spacecraft with two or four flexible booms in symmetric configurations. In general, rearward-positioned and rearward-oriented booms help stabilize the spacecraft, but the spacecraft becomes less stable as boom flexibility increases, particularly for forward oriented booms. Also, depending on the spacecraft body and boom parameters, there are some configurations where the booms actually bend forward into the flow and not backwards as might be expected.