Analytical solutions are presented using method of separation of variables for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of half channel width to Debye length, the periodic EOF electric oscillating Reynolds number Re and normalized relaxation time lambda(1)omega on velocity profiles and volumetric flow rates are presented. Results show that for prescribed electrokinetic width K, lower oscillating Reynolds number Re and shorter relaxation time lambda(1)omega reduces the plug-like EOF velocity profile of Newtonian fluids. For given Reynolds number Re and electrokinetic width K, longer relaxation time lambda(1)omega leads to rapid oscillating EOF velocity profiles with increased amplitude. With the increase of the K, the velocity variations are restricted to a very narrow region close to the EDL for small relaxation time. However, with the increase of the relaxation time, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. As far as volume flow rates are concerned, for given electrodynamic width K. larger oscillating Reynolds number Re results in a smaller volume flow rates. For prescribed oscillating Reynolds number Re, with the changes of relaxation time lambda(1)omega, volume flow rates will produce some peaks no matter how the electrodynamic width K varies. Moreover, the time periodic evolution of the velocity profiles provides a detail insight of the flow characteristic of this flow configuration. (C) 2011 Elsevier B.V. All rights reserved.