The peristaltic transport of Jeffrey fluid through the rectangular duct is investigated. The effect of porosity under the influence of partial slip is also taken into consideration. The equations describing the flow transport along with boundary conditions are first made dimensionless using appropriate transformations and are then solved to get the exact solutions. The role of pressure rise generated by the fluid is also presented. The obtained results are examined graphically through pertinent parameters affecting the flow. The streamlines have also been displayed to analyse the trapping phenomenon.