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In this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very well at large value of time when the ratio is related to fluid parameters γ∗γ>1.