Abstract For the mechanical behavior of poroelastic media, the method of homogenization has been applied to derive effective equations on the macroscale, for a matrix with a periodic structure on the microscale. In existing theories the resulting effective equations are linear, which not only confirm the phenomenological theory of Biot [ J. Appl. Phys. 12 , 155–165 (1941)], but also provide a theoretical framework for calculating the constitutive coefficients. We point out that all past authors applied the continuity of displacement and stresses at the initial and undeformed solid-water interface; this implies that the solid displacement, due either to global or local strain, must be much smaller than the granular or pore size. Here we shall allow the matrix displacement corresponding to the global strain to be comparable to the granular size, and show that the resulting effective equations are non-linear in general. The constitutive coefficients of the non-linear terms nevertheless vanish under two conditions: (i) when the global-scale deformation is also much smaller than the granular size, and (ii) when the global-scale deformation is comparable to the granular or pore size, but the microcell geometry is symmetric with respect to three orthogonal planes. The first limit is trivial and is no different from the existing theories. The second limit is not trivial and shows the robustness of the linearized equations. The result suggests that the linear effective equations may be adequate even for practical problems involving not-too-small deformation or loading, as long as the microscale geometry is isotropic in the statistical sense.