Numerous industrial and biological processes like water filtering, air filtering, blood flow through arteries, and absorption of digested foods are a few examples of flow with suction/injection at the walls. Studies related to the injection/suction of Newtonian fluids have been reported by several researchers in the past, but studies related to the flow of non-Newtonian fluids with injection/suction are scarce in the open literature. Rivlin-Eriksen fluid (also known as third-grade fluids) is an important class of non-Newtonian fluids that is applied for modeling crude and slurry material in a liquid state, molten lava, blood flow, petroleum etc. Considering this, the flow of a Rivlin-Ericksen fluid of grade three through large porous Parallel plates with bottom injection and top suction (same velocity of suction and injection) is analyzed in the present study. The governing equations of fluid flow are solved by using the least square method, which is an important part of the present study. Choosing the trial function for the least square method in this particular case is a difficult task since the velocity profile turns out to be asymmetric for higher velocity of suction and injection. In this study, proper implementation of the least square method is demonstrated for such types of asymmetric velocity distribution, which is a novelty. In the present study a solution for non-dimensional velocity distribution is obtained, and the results are validated with the solution obtained by perturbation method. The results reveal that with an increase in the non-Newtonian parameter (when the cross-flow Reynolds number is low), velocity decreases at the same rate, both near the bottom and top walls. However, when the cross-flow Reynolds number is higher, velocity near the bottom plate is nearly unaffected by a decrease in the non-Newtonian parameter, whereas, near the top plate, velocity decreases with an increase in the non-Newtonian parameter.