Saturated deposits of low permeability soils, when loaded by a surcharge, may lead to settlements taking place over a long period of time. As an example, structures built on alluvial or marine marshy areas, where soft clay deposits frequently occur, may deform at a very slow rate. This phenomenon is known as consolidation and has firstly been studied by Terzaghi in 1914, when teaching at the University of Constantinople. The chapter discusses Terzaghi’s piston-spring-water system analogy, one dimensional consolidation theory, and one dimensional differential equation. Deformation during oedometer compression can be caused by different phenomena. Initial or immediate settlements occur simultaneously with the application of loading. Settlement measurements in foundation of structures the classification of soils types according to secondary settlement. The Casagrande method can be easily applied to clays in the normally consolidated stress range.