Dykes and inclined sheets are known occasionally to exploit faults as parts of their paths, but the conditions that allow this to happen are still not fully understood. In this paper, we report field observations from a swarm composed of 91 segments of dykes and inclined sheets, the swarm being particularly well-exposed in the mechanically layered caldera walls of the Santorini volcano, Greece. Here the focus is on dykes and sheets in the swarm that are seen deflected into faults and the mechanical conditions that encourage such deflections. In particular, we present new analytical and numerical models to explain the mechanical principles of dyke/sheet deflections into faults. The numerical models are applied to a normal-fault dipping 65° with a damage zone composed of parallel layers or zones of progressively stiffer rocks with increasing distance from the fault rupture plane. We model a sheet-intrusion, dipping from 0° to 90° and with an overpressure of alternatively 1 MPa and 5 MPa, approaching the fault. We further tested the effects of changing (1) the thickness of the sheet-intrusion, (2) the fault-zone thickness, (3) the fault-zone dip-dimension (height), and (4) the loading by, alternatively, regional tension and compression. We find that the stiffness of the fault core, where a compliant core characterises recently active fault zones, has pronounced effects on the orientation and magnitudes of the local stresses and, thereby, on the likelihood of dyke/sheet deflection into the fault zone. Similarly, the analytical models, focusing on the fault-zone tensile strength and energy conditions for dyke/sheet deflection, indicate that dykes/sheets are most likely to be deflected into and use steeply dipping recently active (zero tensile-strength) normal faults as parts of their paths. •Detailed field data on dykes and faults in Santorini volcano.•Documented mechanical interactions between dykes, inclined sheets, and faults.•Numerical and analytical models to explain the mechanical interactions.•Fault-zone stiffness controls the attitude of deflected dykes/sheets.•Dyke/sheet deflect primarily into steeply dipping, low-tensile-strength fault zones.