In this paper the dynamical response of cylindrical nanorods to ultrafast laser-induced heating is examined. Theoretical analysis predicts that both extensional and breathing vibrational modes of the rods should be excited by laser-induced heating. Analytical formulas for the frequencies of these modes are derived assuming that the length of the rods is much greater than their radii. Because the frequency of the fundamental extensional mode is much lower than that of the breathing mode, the extensional mode will dominate the response for a real experiment, i.e., for a finite-time heating/expansion process. The results of this model are compared to data from transient absorption experiments performed on gold nanorods with average aspect ratios (length / width) between 2.1 and 5.5, and widths on the order of 10-20 nm. The transient absorption traces show pronounced modulations with a period between 45 and 70 ps, which are only observed when the probe laser is tuned to the longitudinal plasmon band of the sample. The measured periods are in good agreement with the expected period for the extensional modes of the rods. The actual value of the measured period depends on the specific sample and probe laser wavelength. This occurs because the samples are polydisperse, and different length rods absorb in different regions of the spectrum. For rods with widths greater than 20 nm, the breathing mode can also be observed and, again, the measured periods are in good agreement with the theoretical calculations. The breathing mode is not observed for the thinner rods (~10 nm width) because in this case the period is comparable to the timescale for lattice heating in the experiment.