We predict that portions of the New Jersey continental slope were unstable approximately 0.5 million years ago. This instability was caused by rapid sediment loading during a Pleistocene sea-level lowstand and by flow focusing in underlying, permeable Miocene strata. The simulated instability is consistent with soft-sediment deformation and small slumps in Pleistocene strata of the Hudson Apron. Stability of the New Jersey margin has increased since 0.3 Ma because sedimentation rate has decreased. Today, the modelled factor of safety (FS) for the upper slope is approximately 1.5 whereas in the lower slope it exceeds 3. We predict that sedimentation rate is a dominant factor on slope stability. When rapid and asymmetric loading of a highly permeable sedimentary layer occurs, the location of instability can shift seaward to regions where sedimentation rates are low. Stability calculations use pressures and effective stresses predicted by a coupled sedimentation-fluid flow model. This hydrodynamic analysis demonstrates how the interplay of sedimentation and fluid migration affects the distribution, timing, and size of sedimentary failures.