| This paper investigates ballistic motions in walking quadrupeds on a horizontal plane. The study is carried out on a quadruped consisting of a body and four identical two-link legs. Each leg has a knee joint and is connected to the body by a haunch joint. Three types of quadruped gaits, bound, amble, and trot, are studied. None of these gaits complies a flight phase, but they all involve simultaneous and identical motion of two legs. Muscle activities are commonly believed to alternate with periods of relaxation. Our study, therefore, assumes that the swing phase is ballistic, i.e., no active control torque is exerted. Ballistic motion is achieved through appropriate initial velocities. These velocities result from impulsive active control torques and ground reactions exerted at the boundary instants of the single support phase. Natural ballistic motions are shown to exist for the three gaits and for each valid walking velocity class. Torque cost analysis shows that amble and trot gaits are more efficient than bound.