Soil surrounding a submarine buried pipeline consolidates as ocean waves propagate over the seabed surface. Conventional models for the analysis of soil behaviour near the pipeline assume a two-dimensional interaction problem between waves, the seabed soil, and the structure. In other words, it is often considered that water waves travel normal to the orientation of pipeline. However, the real ocean environment is three-dimensional and waves approach the structure from various directions. It is therefore the key objective of the present research to study the seabed behaviour in the vicinity of marine pipelines from a three-dimensional point of view. A three-dimensional numerical model is developed based on the Finite Element Method to analyse the so-called momentary behaviour of soil under the wave loading. In this model, the pipeline is assumed to be rigid and anchored within a rigid impervious trench. A non-slip condition is considered to exist between the pipe and the surrounding soil. Quasi-static soil consolidation equations are then solved with the aid of the proposed FE model. In this analysis, the seabed behaviour is assumed to be linear elastic with the soil strains remaining small. The influence of wave obliquity on seabed responses, i.e. the pore pressure and soil stresses, are then studied. It is revealed that three-dimensional characteristics systematically affect the distribution of soil response around the circumference of the underwater pipeline. Numerical results suggest that the effect of wave obliquity on soil responses can be explained through the following two mechanisms: (i) geometry-based three-dimensional influences, and (ii) the formation of inversion nodes. Further, a parametric study is carried out to investigate the influence of soil, wave and pipeline properties on wave-associated pore pressure as well as principal effective and shear stresses within the porous bed, with the aid of proposed three-dimensional model. There is strong evidence in the literature that the failure of marine pipelines often stems from the instability of seabed soil close to this structure, rather than from construction deficiencies. The wave-induced seabed instability is either associated with the soil shear failure or the seabed liquefaction. Therefore, the developed three-dimensional FE model is used in this thesis to further investigate the instability of seabed soil in the presence of a pipeline. The widely-accepted criterion, which links the soil liquefaction to the wave-induced excess pressure is used herein to justify the seabed liquefaction. It should be pointed out that although the present analysis is only concerned with the momentary liquefaction of seabed soil, this study forms the basis for the three-dimensional analysis of liquefaction due to the residual mechanisms. The latter can be an important subject for future investigations. At the same time, a new concept is developed in this thesis to apply the dynamic component of soil stress angle to address the phenomenon of wave-associated soil shear failure. At this point, the influence of three-dimensionality on the potentials for seabed liquefaction and shear failure around the pipeline is investigated. Numerical simulations reveal that the wave obliquity may not notably affect the risk of liquefaction near the underwater pipeline. But, it significantly influences the potential for soil shear failure. Finally, the thesis proceeds to a parametric study on effects of wave, soil and pipeline characteristics on excess pore pressure and stress angle in the vicinity of the structure.