We analyze the effect of the host crystal symmetry on the optical spectra of the 6P(1/2)-6S(1/2) and 6P(3/2)-6S(1/2) transitions of atomic Cs in solid (4)He matrices. In particular, we address the deformation of the bubble structures formed by Cs in such quantum crystals. We show that the anisotropy of the stiffness tensor leads to static quadrupolar bubble shape deformations in hexagonally close-packed (hcp) crystals, while the corresponding deformations in the body-centered cubic (bcc) phase of the matrix have a hexadecupolar symmetry. A comparison of the measured excitation spectra with our model calculations allow us to infer quantitative values of the deformation parameters.