Maurice A. Biot's 1955 paper extends his earlier theory of elasticity and consolidation for isotropic materials to anisotropic solids. The paper introduces a general method for deriving equations that describe the behavior of porous, anisotropic solids under load. It discusses the case of transverse isotropy and complete isotropy, showing how the equations simplify in these cases. The theory is applicable to predicting the time history of stress and strain in porous solids with fluid flow. The paper also presents general equations for the anisotropic case, including the stress tensor and strain components for both solid and fluid phases. The theory is applied to the case of transverse isotropy, which is particularly relevant to soils and rock formations. The paper also discusses the case of isotropy, where the equations reduce to a simpler form. The paper concludes by showing that the equations derived for the anisotropic case are consistent with those derived for isotropic materials. The paper also discusses the application of the theory to specific cases and the use of operational calculus for solving consolidation problems. The paper is part of a series of studies on the theory of elasticity and consolidation for porous materials.Maurice A. Biot's 1955 paper extends his earlier theory of elasticity and consolidation for isotropic materials to anisotropic solids. The paper introduces a general method for deriving equations that describe the behavior of porous, anisotropic solids under load. It discusses the case of transverse isotropy and complete isotropy, showing how the equations simplify in these cases. The theory is applicable to predicting the time history of stress and strain in porous solids with fluid flow. The paper also presents general equations for the anisotropic case, including the stress tensor and strain components for both solid and fluid phases. The theory is applied to the case of transverse isotropy, which is particularly relevant to soils and rock formations. The paper also discusses the case of isotropy, where the equations reduce to a simpler form. The paper concludes by showing that the equations derived for the anisotropic case are consistent with those derived for isotropic materials. The paper also discusses the application of the theory to specific cases and the use of operational calculus for solving consolidation problems. The paper is part of a series of studies on the theory of elasticity and consolidation for porous materials.