The optimal response of the Batchelor vortex is studied by considering the time-harmonically forced problem with frequency omega. High variance levels are sustained in this system under periodic forcing. The optimal response is largest when the input frequency is null in the axisymmetric case (m= 0). In addition, the axial flow does not play a relevant part in determining the optimal response. When considering helical modes vertical bar m vertical bar = 1, perturbations are excited through a resonance mechanism at moderate and large wavelengths. At smaller wavelengths, a large response is excited by steady forcing. Regarding the axial flow, the response is largest when the axial velocity intensity is near to zero. For perturbations with larger azimuthal wavenumbers vertical bar m vertical bar > 1, the magnitude of the response is smaller than those for helical modes. Therefore, studying the response for vertical bar m vertical bar > 1 is of no interest. Published by AIP Publishing.