A compact form for the condition of mechanical equilibrium for arbitrary curved interfaces has been formulated in the case when the bulk pressures are non-diagonal local tensors. This form of the condition is applicable to a non-spherical interface between fluid or solid phases, without or with arbitrary number of any external fields. The equilibrium condition has been transformed into a set of differential equations for the tangential and transverse components of the mechanical surface tension and bulk pressure tensors at a dividing surface. One condition simplifies to the usual Laplace equation of capillarity for the transverse direction across the interface, while the other conditions relate to the tangential equilibrium state of the fluid. The amendment of the definition of a dividing surface has been given.