We discuss forward and backward modes in one-dimensional (1-D) periodic bounded structures. First, it is shown that the conventional definition of the phase speed can incorrectly identify the forward/backward nature of modes. Therefore, we propose an alternative definition of the phase speed for modes in bounded periodic structures and demonstrate that this definition correctly identifies the nature of modes in a 1-D periodic corrugated parallel plate waveguide. The proposed phase speed is analyzed through simulations with commercial software and a circuit model.