The Oxford Dictionary of Earth Sciences describes 'confining pressure' as "the combined hydrostatic stress and lithostatic stress; i.e. the total weight of the interstitial pore water and rock above a specified depth." Confining pressure might influence ductile behavior of rocks as well. Ductile behavior is enhanced where high confining pressures are combined with high temperatures and low rates of strain, conditions characteristic of deeper crustal levels.
The overburden pressure at a depth z is given by
In deriving the above equation it is assumed that gravitational acceleration g is a constant over z, since it is placed outside the integral. In reality, g is a (non-constant) function of z and should appear inside the integral. But since g varies little over depths which are a very small fraction of the Earth's radius, it is placed outside the integral in practice for most near-surface applications which require an assessment of lithostatic pressure. In deep-earth geophysics/geodynamics, gravitational acceleration varies significantly over depth and g may not be assumed to be constant.
This should be compared with the equivalent concept of hydrostatic pressure in hydrodynamics.