Fault geometry and kinematics indicate that two different tectonic regimes affected the late Pliocene volcanic succession around the Thverfell magmatic complex (Esja peninsula, SW Iceland): The older phase is characterized by sets of left-lateral strike-slip, E–W- to ESE-striking faults and right-lateral strike-slip, N–S- to NE-striking faults; the younger phase produced normal dip-slip, NNE-striking faults. Stress tensor calculation for the older regime provides a horizontal, NE- to E–W-trending greatest principal stress (σ1) and a horizontal NW- to N–S-trending least principal stress (σ3), followed by a stress regime change with a vertical σ1 and a WNW-trending σ3. Structural–stratigraphic analyses of the eroded Thverfell magmatic complex indicate three main systems, namely (i) a centrally-dipping sheet swarm, E–W-elongated in plan view, (ii) a sill-composed laccolith, fed by E–W-striking dikes, and (iii) NNE- to NE-striking dikes offsetting the previous intrusions. These data allow unravelling of a multiphase history of magma-tectonics interaction. First, an excess magma pressure from an underlying magma chamber induced the emplacement of the centrally-dipping sheets; this was accompanied by magma upwelling along dikes that bent to propagate as sills under the influence of stress and rheological barriers induced by the lava overburden. Finally, regional dikes linked to the WNW-trending rift extension were emplaced.