One of the main concerns regarding the development of submarine landslides is the role played by weak layers in the failure process and, in particular, their impact in terms of volume, shape, and evolution of mass movements. In the present study we identified a weak layer in the eastern margin of the Corsica Trough (northern Tyrrhenian Sea) that formed the basal failure surface of the Pianosa Slump at 42–50 ka. This layer is characterized by high water content, high plasticity, high compressibility, and post-peak strain softening behavior (i.e., strength loss with increasing strain). These specific mechanical and sedimentological properties seem to be related to the presence of analcime zeolites with a concentration of 2–4% in the muddy sediment. Zeolites commonly form by the alteration of volcanic rocks and were deposited on the slope during a sea level low-stand. The influence of the zeolitic layer on slope instability was tested numerically using an elastic-perfectly plastic model that exhibits strain softening. Modeling results show that erosion at the foot of the slope could lead to enough strain to reduce the shear strength of the zeolitic layer and lead to slip in this layer. We conclude that the strain softening behavior of muddy zeolitic sediment plays an important role in predisposing submarine landslides on continental slopes.