This paper clarifies vibration response characteristics of a vertical mechanical structure subjected to horizontal and vertical nonstationary random excitation. The structure is modeled as a cantilever beam with a lump mass at its free end; taking into account the first vibration mode for numerical computation of vibration response, response multiplication factor maps with respect to dominant frequencies, omega //H and omega //v, of both horizontal and vertical excitations are obtained for the structure's damping, magnitude and randomness of vertical excitation. A very high response appears at omega //v equals 2 and omega //H equals 1 and its magnitude varies with a slight change in the power spectral density contained in nonstationary vertical excitation waves at omega //v equals 2. For omega //v equals 2 and omega //H equals 1, the conditions of unstable parametric random vibration are obtained for structure damping and magnitude of vertical excitations.