The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by a laser interferometer below 8 MHz. These resonances correspond to Zero-Group Velocity guided modes or to circumferential modes. The authors observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifests as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured ones, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted, leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.