Within the context of the structural-temporal approach, the dynamic effects of the strength characteristics of rocks arising due to hydrostatic pressure are analysed. The key idea of the proposed approach is the introduction of the incubation time parameter for describing material fracture processes, which is interpreted as the main measure of material response. Theoretical velocity dependencies of the fracture toughness for marble and granite, subjected to different values of external hydrostatic pressure, as well as for dry and wet sandstones, are predicted based on the proposed approach. The calculated incubation times for marble and granite are allowed to establish a linear function between incubation time and hydrostatic pressure. The obtained values of incubation times are compared according to the velocity dependencies of the fracture toughness and the velocity dependencies of the strength of rocks differing in external hydrostatic pressure or moisture level. It is shown that the incubation time depending on the external hydrostatic pressure or on the moisture of rocks is similarly changed.