Experimental consolidation of uncemented clay‐rich marine sediments provides information concerning their stress history. A main finding is that some of the well‐known behavior of soft sediment deformation in geotechnical applications cannot validly be extrapolated to sediments that have been subjected to higher stresses and longer times of geologic conditions. This study confirms that the yield stress of the uncemented sediment accurately reflects its previous maximum consolidation state. Furthermore, we have identified a new phase of post‐yield strain that is associated with higher values of the modified compression index (the slope of the porosity versus the logarithm of effective vertical stress) than that of elastic deformation, but with much lower values than that for primary consolidation. This post‐yield behavior is a linear, non‐elastic deformation, and is termed tertiary consolidation. Yield stress appears independent of creep time or strain rate, whereas the tertiary‐primary consolidation transition is sensitive to these parameters. During post‐yield creep (secondary consolidation) the slope of the porosity versus the logarithm of time curve, or the secondary consolidation index, is generally assumed constant. However, this is not valid for claystones at effective vertical stresses above about 1 MPa, where the secondary consolidation index increases with stress. At a given effective vertical stress, the secondary consolidation index also increases with creep times greater than about 105 s (≈28 h).