The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments. The configurations of near space hypersonic flying vehicles are rather different from those of conventional aircrafts. Their configurations are relatively slender; hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes, resulting in strong coupling of rotations around the three axes.Thus, the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts, and there is no available result of stability analysis which can be readily applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation, of our rolling stability of flying vehicle under known pitching motion. stability criterion of rolling motion is obtained with and without lateral motions. We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-St okes equations coupled with dynamic equations of flight. The results of simulation agree well with those of theoretical analysis and experiments.