Simplified models were widely used for analysis of peristaltic transport caused by contraction and expansion of an extensible tube. Each of these models has its own assumptions, and therefore, weakness. To get rid of the limitations imposed by the assumptions, a numerical procedure is employed to simulate this pumping flow in the present study. In earlier studies, the frame of reference adopted moves with the peristaltic speed of the vibrating wall so that the flow becomes steady. The flow characteristics in a wavelength were the main concern. In our calculations, a channel of finite length with a flexible wall is considered. Pressures are prescribed at the inlet and outlet boundaries. The computational grid is allowed to move according to the oscillation of the wall. Another state-of-the-art technique employed is to construct the grid in an unstructured manner to deal with the variable geometry of the duct. The effects of dimensionless parameters, such as amplitude ratio, wave number, Reynolds number, and back pressure on the pumping performance are examined. Details of the peristaltic flow structure are revealed. Also conducted is the comparison of numerical results with the theoretical predictions obtained from the lubrication model to determine the suitability of this theory.