A linear theory of elastic materials with voids is presented, which differs from classical linear elasticity by treating the volume fraction corresponding to voids as an independent kinematic variable. The theory is formulated with basic equations, and boundary-value problems are considered, establishing uniqueness and weak stability for the mixed problem. Applications include homogeneous deformations, pure bending of beams, and small-amplitude acoustic waves, where the change in void volume due to deformation is analyzed. The relationship between this theory and the effective moduli approach for porous materials is discussed. The theory is based on the concept of bulk density as the product of matrix density and volume fraction, introducing an additional kinematic degree of freedom. It uses the same balance equations as Goodman and Cowin, including a volumetric rate effect possibly due to inelastic surface effects near void boundaries. The non-linear theory of [1] is linearized in the Appendix. Section 3 discusses solution boundedness and establishes uniqueness and weak stability for the mixed boundary-value problem. Section 4 studies homogeneous deformations, showing stress-strain response analogous to viscoelastic materials, and that quasi-static deformations are only possible in symmetric materials. Section 5 considers static pure bending of beams, finding that plane sections remain plane but stress distribution is non-linear due to void volume changes. Section 6 describes acoustic wave properties, showing transverse waves propagate without affecting porosity, while longitudinal waves are attenuated and dispersed due to porosity changes. Two types of longitudinal waves are possible, one related to matrix properties and one to void properties. The final section discusses the relationship between the theory and effective moduli calculations for porous materials, suggesting they are complementary. The linear theory of elastic materials with voids is described in Section 2, dealing with small changes from a reference configuration, with bulk density, matrix density, and volume fraction related by ρ_R = γ_R ν_R. The independent kinematic variables are displacement field u_i and volume fraction change φ. The equations of motion are the balance of linear momentum, ρ ü_i = T_ij,j + ρ b_i.A linear theory of elastic materials with voids is presented, which differs from classical linear elasticity by treating the volume fraction corresponding to voids as an independent kinematic variable. The theory is formulated with basic equations, and boundary-value problems are considered, establishing uniqueness and weak stability for the mixed problem. Applications include homogeneous deformations, pure bending of beams, and small-amplitude acoustic waves, where the change in void volume due to deformation is analyzed. The relationship between this theory and the effective moduli approach for porous materials is discussed. The theory is based on the concept of bulk density as the product of matrix density and volume fraction, introducing an additional kinematic degree of freedom. It uses the same balance equations as Goodman and Cowin, including a volumetric rate effect possibly due to inelastic surface effects near void boundaries. The non-linear theory of [1] is linearized in the Appendix. Section 3 discusses solution boundedness and establishes uniqueness and weak stability for the mixed boundary-value problem. Section 4 studies homogeneous deformations, showing stress-strain response analogous to viscoelastic materials, and that quasi-static deformations are only possible in symmetric materials. Section 5 considers static pure bending of beams, finding that plane sections remain plane but stress distribution is non-linear due to void volume changes. Section 6 describes acoustic wave properties, showing transverse waves propagate without affecting porosity, while longitudinal waves are attenuated and dispersed due to porosity changes. Two types of longitudinal waves are possible, one related to matrix properties and one to void properties. The final section discusses the relationship between the theory and effective moduli calculations for porous materials, suggesting they are complementary. The linear theory of elastic materials with voids is described in Section 2, dealing with small changes from a reference configuration, with bulk density, matrix density, and volume fraction related by ρ_R = γ_R ν_R. The independent kinematic variables are displacement field u_i and volume fraction change φ. The equations of motion are the balance of linear momentum, ρ ü_i = T_ij,j + ρ b_i.