In the development of offshore oil and gas deepwater field, pipelines are often laid directly on the sea bed. The initial embedment generated during installation is the basic data for stability and lateral buckling calculation, making it particularly important to evaluate the initial embedment of pipelines accurately. This paper studies the initial embedment of submarine pipeline in clay environment using the Coupled Eulerian-Lagrangian(CEL) method in finite element software ABAQUS. The DNV-RP-F114 Pipe-soil interaction for submarine pipelines(hereinafter referred to as DNV-RP-F114) method is used for comparison and verification. The study clarifies the morphological changes, stress response and the development pattern of plastic zones in the clay seabed during pipeline sinking. Additionally, the influence of soil with different strengths and friction coefficients on the initial embedment of pipeline is analyzed. The results show that, compared with the DNV-RP-F114 method, the initial embedment calculated using the CEL method is smaller. The numerical model conforms to the soil mechanics principles, showing that the pipeline initial embedment is significantly affected by soil strength, while the change of friction coefficient has a minimal effect. The research results can provide reference for the analysis of initial embedment of submarine pipelines and guidance for the structural design of submarine pipelines.