In this work, the linear stability analysis of a pulsed Taylor-Couette flow is investigated in the case of a linear Maxwell fluid when both cylinders are subjected to an out-of phase modulation with equal modulation amplitude and equal modulation frequency. The linear problem is solved using the Floquet theory and a technique of converting a boundary value problem to an initial value problem. Attention is focused on the influence of elasticity on the critical parameters corresponding to the onset of instability. The numerical results show that the Deborah number has a destabilizing effect in the high frequency limit and the critical parameters are independent on the frequency number. However, in the low frequency limit the Maxwell fluid behaves as a Newtonian one and no effect of Deborah number is observed.
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