One of the problems of major concern in designing large oil storage tanks is the interaction with the foundation soil, particularly in terms of differential settlements. Ultimate or serviceability limit states can be reached due to nonallowable local displacements along the tank perimeter. This paper presents experimental data obtained during the construction of a thermal power plant in Northern Italy. The performed analyses have been particularly devoted to highlighting the occurrence of local soil yielding and its influence on the performance of oil tank structures. The analyses address the influence of local soil yielding on excess pore pressure response as well as on the trend of lateral displacements and perimeter differential settlements. As soon as the soil reaches a yielding condition, significant changes occur in terms of the overall soil-structure interaction phenomena, with consequences mainly in the displacement patterns and rates. The obtained evidence reported in the paper is aimed to focus the attention of the designer on the need to properly detect the stress history of the soil deposit.