The objective of this work is a numerical analysis of chaotic mixing in the two-dimensional channel flows. For the analytical flow models, the pulsatile flow through a rough-wall channel and the autonomous oscilating flow through a buffled channel were considered. As the considered flow models are two-deimensional, we have a stream function ψ(x,y,t), and the equations of motion of an advected particle are simply x=аψ/ay, y=-aψ/ax. These equations have the form of Hamilton's canomical equations for a dynamical system with one or two degree of freedom. Chaotic phenomena for the flow models were investigated by using Poincare map and Liapunov exponents which are typical method for analysing dynamical systems. In addition, the relation of flows between the Eulerian and the Lagrangian representations was discussed. The obtained results showed that the chaotic motion of an advected particle was demonstrated even when simply flow structure of a time-periodically fluctuated flow, from view of Eulerian representation, then chaotic mixing (stretching and folding of fluid element) can be produced consequently.