Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated. The rheological characteristics are characterized by the constitutive equations of a power-law fluid. Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments. Exact solutions are established for the stream function and velocity. The streamlines pattern and trapping are given due attention. Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.