The laboratory miniature vane shear test (MVST) has been widely used to measure the undrained shear strength of marine sediments in offshore engineering. However, the transfer of the soil sample in tube samplers from the seabed to the laboratory releases the in situ confining stress acting on the soil and will decrease the soil strength. In this research, in order to investigate the effects of confining stress on the undrained shear strength of marine sediments, the Coupled Eulerian-Lagrangian (CEL) approach in ABAQUS is used to model the three-dimensional standard and miniature vane shear tests to estimate the undrained shear strength of sensitive clay with different sensitivities under various stress conditions. Based on the numerical simulation results, a linear strength model that not only considers confining stress effects but also can eliminate the size effects caused by vane blades of MVST is proposed. The proposed model can be used to estimate the undrained shear strength of the sensitive clay under shallow seabed surfaces.