The biomicro fluidic devices utilizing electroosmosis for flow actuation are usually encountered with non-Newtonian behavior of working uids. Hence, studying the  flow of non-Newtonian fluids under an electroosmotic body force is of high importance for accurate design and active control of these devices. In this paper, mixed electroosmotically and pressure driven flow of two viscoelastic uids, namely PTT and FENE-P models, through a rectangular microchannel is examined. The governing equations in dimensionless form are numerically solved through a finite dierence procedure for a non-uniform grid. It is observed that although the Debye-Huckel linearization fails to predict the velocity prole for viscoelasticuids, this approximation holds even at high zeta potentials, provided the velocity field is normalized with the mean velocity. It is also revealed that the dependency of the mean velocity on the level of elasticity in the fluid is linear. This functionality results in a Poiseuille number independent of the level of elasticity in the fluid. Moreover, the pressure eects are pronounced for higher values of the channel aspect ratio. In addition, both the mean velocity and the Poiseuille number are increasing functions of the channel aspect ratio.