As the first paper of a series on the content update of European and American classic mechanics textbooks for science majors, this manuscript explores the formation of traditional teaching contents via the analysis on 10 textbooks. After the physics revolution at the beginning of the last century, the textbooks of mechanics in classical physics were titled as classical mechanics after the 1950s. In order to lay the foundations of mechanics and mathematics for modern physics, classical mechanics courses formed a steady traditional teaching content in the 1950s and 1960s. Its theories include Newton mechanics, Lagrange mechanics, and Hamilton mechanics. Its problems include particle motions in a central force field, particle motions in non-inertial frames, rigid-body 3-dimensional motions, and vibrations of discrete and continuous systems.