In this investigation, we discuss the peristaltic motion based on the constitutive equations of a Carreau fluid in a channel. The fluid is electrically conducting in the presence of a uniform applied magnetic field. Four different wave forms are chosen. The fluid behaviour is studied using long wavelength approximation. Detailed analysis is performed for various emerging parameters on pumping and trapping phenomena. The present results reduce favourably with the currently available results of hydrodynamic case when the Hartman number is chosen zero.