Recent studies hypothesize that some submarine slides fail via pressure‐driven slow‐slip deformation. To test this hypothesis, this study derives pore pressures in failed and adjacent unfailed deep marine sediments by integrating rock physics models, physical property measurements on recovered sediment core, and wireline logs. Two drill sites (U1394 and U1399) drilled through interpreted slide debris; a third (U1395) drilled into normal marine sediment. Near‐hydrostatic fluid pressure exists in sediments at site U1395. In contrast, results at both sites U1394 and U1399 indicate elevated pore fluid pressures in some sediment. We suggest that high pore pressure at the base of a submarine slide deposit at site U1394 results from slide shearing. High pore pressure exists throughout much of site U1399, and Mohr circle analysis suggests that only slight changes in the stress regime will trigger motion. Consolidation tests and permeability measurements indicate moderately low (~10−16–10−17 m2) permeability and overconsolidation in fine‐grained slide debris, implying that these sediments act as seals. Three mechanisms, in isolation or in combination, may produce the observed elevated pore fluid pressures at site U1399: (1) rapid sedimentation, (2) lateral fluid flow, and (3) shearing that causes sediments to contract, increasing pore pressure. Our preferred hypothesis is this third mechanism because it explains both elevated fluid pressure and sediment overconsolidation without requiring high sedimentation rates. Our combined analysis of subsurface pore pressures, drilling data, and regional seismic images indicates that slope failure offshore Martinique is perhaps an ongoing, creep‐like process where small stress changes trigger motion.