Abstract In this work, the dynamic characteristics of the human skull-brain system are studied. For the purpose of our analysis, we adopted a model consisted of a hollow sphere (skull), an inviscid and irrotational fluid (cerebrospinal fluid), and a concentrically located inner elastic sphere (brain). The mathematical analysis is based on the elasticity solution for the elastic spheres and the simplified description of the motion of the fluid by the wave equation. The roots of the characteristic equation were found numerically. The results are in agreement with other researchers analogous modelling work, however our three-dimensional analysis introduces a new pattern of frequencies to the natural frequencies spectra of the skull-brain system. The results are compared with experimental ones and the role of the various system parameters on the natural frequencies is investigated.