The oil production in Russia will be gained due to the field development in the Northwestern Federal District, Siberian Federal District, and Far Eastern Federal District. The remoteness of natural gas consumers from these Districts stimulates the development of pipeline transportation. A long range of pipelines and climatic and geological conditions result in toughening up the requirements for their reliability and lifetime improvement. Giant oil-gas condensate fields that have been discovered for the past few years in northern and central parts of the Caspian Sea are very promising in the light of onshore field depletion and increasing the demand for petroleum. 19% of the Caspian Sea shoreland, i.e. approx. 4,1 billion tons of oil equivalent belong to the Russian Federation. In the opinion of some experts, one third of the world hydrocarbon reserves falls on deposits in the Caspian Sea A host of deposits discovered in the Caspian Sea is located on the sea shelve. The oil extraction in the sea shelve is 2-3 times more expensive than onshore extraction owing to the high-technologies and more efficient equipment required for the development of underwater oil-gas deposits. In northern shallow-water area of the Caspian Sea that belongs to Russia, the oil extraction is more convenient and expedient than in its depth However, the following reasons complicate the oil-gas development in this area: 1. The northern shallow-water area (not deeper than 20 m) is strongly contaminated with oil products due to the pipeline buckling in soft soil. 2. In winter, this area experiences the complicated ice conditions that results in damage of the unprotected equipment and underwater pipelines. 3. The recent years have seen a lot of accidents connected with the dense traffic that results in damages of unburied pipelines. Consequently, in the Caspian Sea it is impossible to lay pipelines on the seabed and advisable to lay them inside trenches. The current regulatory documents do not contain an explicit design technique of laying underwater pipelines in soft soils. A strength testing methodology of water-deposited soil is not provided as well as its load-bearing capacity in relation to underwater pipelines. This paper mainly focuses on the analysis of the stress-strain state of offshore pipelines laid in water-deposited soil to select the optimum parameters of pipeline trenching. Bottom soil erosion is caused by the hydrodynamic effect. Bottom flows can be constant, tidal and other, depending on the flow rate and direction and the quality of the given soil. Bottom flows can result in the bed movement that, in turn, leads to the formation of cavities, hoppers, channels, and hollows. Underwater soil erosion facilitates the pipeline uncovering and washes away the soil from under the pipes. Cavities rapidly propagate along the pipes resulting in the space formation of considerable length. These processes involve changes in the stress-strain state of the pipe.