  A linear system of differential equations describing a joint motion of
elastic porous body and fluid occupying porous space is considered. Although
the problem is linear, it is very hard to tackle due to the fact that its main
differential equations involve non-smooth oscillatory coefficients, both big
and small, under the differentiation operators. The rigorous justification,
under various conditions imposed on physical parameters, is fulfilled for
homogenization procedures as the dimensionless size of the pores tends to zero,
while the porous body is geometrically periodic. As the results, we derive
Biot's equations of poroelasticity, equations of viscoelasticity, or decoupled
system consisting of non-isotropic Lam\'{e}'s equations and Darcy's system of
filtration, depending on ratios between physical parameters. The proofs are
based on Nguetseng's two-scale convergence method of homogenization in periodic
structures.
