It is pointed out that oscillating current density, produced due to the coupling between an external magnetic field and the cosmic axion field, can excite the TM resonant modes inside an open-ended cavity (tube). By systematically solving the field equations of axion-electrodynamics we obtain explicit expressions for the oscillating fields induced inside a cylindrical tube. We calculate the enhancement factor when a resonance condition is met. While the power obtained for TM modes replicates the previous result, we emphasize that the knowledge of explicit field configurations inside a tube opens up new ways to design axion experiments including a recent proposal to detect the induced fields using a superconducting LC circuit. In addition, as an example, we estimate the induced fields in a cylindrical tube in the presence of a static uniform magnetic field applied only to a part of its volume.