This paper presents the study on the self-weight consolidation, which is referred to the consolidation problem of cohesive deposits in reservoirs and based on Gibson's theory of non-linear finite-strain consolidation. The analytical solution of the linearized equation is carried out. The solution shows that the consolidation is dominated by the dimensionless thickness of soil Zd. When Zd is large, consolidation progresses faster. A mathematical model based on the full equation is set up, which is verified by data and can predict the self-weight consolidation with the thickness increasing with time. The final profile of void ratio is also obtained theoretically. Subsequently, the final thickness of deposits and the final gradient of void ratio are obtained. The comparisons between the analytical solution of linearized equation and the numerical solution of full equation show that the linearization is valid for the small thickness. In addition existing literature on consolidation are reviewed and the Gibson's theory which is based in this study is presented in detail.