This paper presents results of a comprehensive study from first principles into the properties of Ni, Pd, Rh, and Ir crystals under pressure. We calculated elastic constants, phonon spectra, isotherms, Hugoniots, sound velocities, relative structural stability, and phase diagrams. It is shown that in nickel and palladium under high pressures (>0.14 TPa) and temperatures (>4 kK), the body-centered cubic structure is thermodynamically most stable than of the face-centered cubic one. Calculated results suggest that nickel under Earth-core conditions (P∼0.3 TPa, T∼6 kK) have a bcc structure. No structural changes were found to occur in Rh and Ir under pressures to 1 TPa at least. This paper also provides estimations for the pressure and temperature at which the metals of interest begin to melt under shock compression.