Translation and bend of the spine in the sagittal plane during high-speed quadruped running were investigated. The effect of the two spine motions on slip between the foot and the ground was also explored. First, three simplified sagittal plane models of quadruped mammals were studied in symmetric bounding. The first model's trunk allowed no relative motion, the second model allowed only trunk bend, and the third model allowed both bend and translation. Next, torque was introduced to equivalently replace spine motion and the possibility of foot slip of the three models was analyzed theoretically. The results indicate that the third model has the least possibility of slip. This conclusion was further confirmed by simulation experiments. Finally, the conclusion was verified by the reductive model crawling robot.