The impact of spherical symmetry breaking and crystallinity on the response of the vibrational acoustic modes of a nanoobject in frequency- and time-domain experiments is investigated using the finite-element analysis method. The results show that introduction of shape anisotropy, i.e., evolution from a nanosphere to a nanorod, modifies the periods of the fundamental radial and quadrupolar modes and leads to activation of a quadrupolar-like mode in time-domain studies. In contrast, crystallinity is shown to have a negligible impact on the breathing mode frequency of a nanosphere formed by a cubic crystal and does not activate any quadrupolar mode. The effect of an anisotropic excitation in time-resolved measurements of a large nanosphere is also discussed.