Vertical seabed penetration and lateral movement of deep-water offshore pipelines are simulated using the Coupled Eulerian–Lagrangian (CEL) approach in Abaqus finite element (FE) software. Abaqus CEL has been used in some previous studies to simulate large-deformation behavior of offshore pipelines; however, the effects of strain rate and strain-softening on undrained shear strength (su) have not been considered. In this study, the effects of these factors are critically examined. The available built-in models in Abaqus CEL cannot account for these factors directly, especially the strain rate; therefore, the development of user subroutines is required. In the present study, a simple but realistic soil constitutive model (published by Zhou and Randolph in 2007) that considers the effects of strain rate and strain-softening on su is implemented in Abaqus CEL. The effects of FE mesh size and shear band formation on penetration resistance are discussed based on a comprehensive FE simulation. Lateral analyses are performed for “light” and “heavy” pipes in clay seabed having a linearly increasing undrained shear strength profile for smooth and rough pipe–soil interface conditions. The FE results are compared with previous theoretical, numerical, and centrifuge test results. Based on the present FE analyses, it is shown that, similar to the remeshing and interpolation techniques with small strain (RITSS) technique developed at the The University of Western Australia, the Abaqus CEL can successfully simulate the response of partially embedded pipelines in deep-water clay seabed, provided strain rate and softening dependent clay models are implemented. A methodology to implement such a model using Abaqus user subroutine is also presented.