Thirty-six flax fibre-reinforced epoxy (FFRE) plates with two, three, and four fabric layers and lengths ranging from 160 mm to 270 mm and nine FFRE tubes with a diameter of 60 mm, a length of six times the tube diameter plus an overly of 50 mm with two, three, and four fabric layers were manufactured. One-hundred-eighty impulse excitation tests were conducted on FFRE plates to determine the dynamic properties of the plates in the bending mode, and 91 impulse excitation tests were conducted on the FFRE tubes to determine the dynamic properties of the tubes in the transverse, torsional, and longitudinal directions. FFRE plates showed up to six times larger specific energy capacities compared to counterpart glass fibre-reinforced polymer plates, showing significant potential for FFRE plates to replace the use of GFRP plates where considerable damping of energy is required. The results showed that the damping ratio of the FFRE plates decreased with the increase in layers and natural frequency. For the FFRE tubes, the highest damping ratio belonged to the transverse vibration mode, followed by the torsional or longitudinal vibration modes.