Despite considerable ongoing efforts, accurate computational simulation of the flow behavior of (unvulcanized) rubber remains an open challenge. There is growing evidence that one of the reasons for that is insufficient consideration of, or knowledge on, the mechanical compressibility of the material. As a contribution to tackle this open question, we here report on a series of hydrostatic compression tests performed on natural rubber, as well as on two types of EPDM (ethylene-propylene-diene-monomer) rubber compounds. These materials were filled into a capillary rheometer with closed extrusion canal, and then compressed and released through volume changes realized at different speeds, while monitoring the corresponding hydrostatic pressures acting on the investigated rubbers. The volume changes then entered various relevant strain measures (Green-Lagrange strains, Hencky strains, linearized strains), while the pressures were mathematically transformed into energetically conjugate stress measures (second Piola-Kirchhoff stress, Kirchhoff stress, Cauchy stress). Insertion of these measures into the dissipation inequality resulting from the two fundamental laws of thermodynamics, revealed that the investigated materials behave purely elastically under hydrostatic pressure, albeit in a non-linear fashion. Irrespective of the format chosen for elasticity theory, the elastic bulk modulus appears as a power function of the hydrostatic pressure; the former increasing under-linearly, but non-asymptotically, with the latter. Careful statistical evaluation of the corresponding power law coefficients allows for derivation of upper and lower bounds of the bulk modulus, as functions of the hydrostatic pressure, an information which may prove essential for improving the accuracy of rubber extrusion simulations. (C) 2017 Elsevier Ltd. All rights reserved.