During volcanic unrest, high magma pressure induces cracking and faulting of the country rock, providing conduits for the transport of magma and other fluids. These conduits, known as dykes, are fundamental structures for the transport of magma to the surface in volcanically active regions. The mechanics of dyke propagation is not yet fully understood but is crucial to better model dyke emplacement and eruption in volcanoes. Central to this need is a greater understanding of the mechanical properties of the magma/country rock interaction as a function of known magmatic pressure, temperature and stress. Here, we report data from a series of experiments in which we cyclically compress viscoelastic rhyolitic magma (at 828 °C, 892 °C and 918 °C) inside a cylindrical conduit-like shell of basalt (from Mt. Etna, Italy) until fracture occurs. The compression is performed under strain rates cyclically varying between 5×10−6 and 5×10−5 s−1. The resultant monitored (axial) loading and relaxation illustrates how the presence of a visco-elastic fluid (magma) controls the stress induced at the conduit margin boundary. This is achieved by analysing the viscoelastic relaxation (through time) to calculate an apparent modulus, which is found to decrease with both increasing temperature and time. In the 4 cycles before failure we find that the apparent modulus decreases from 180 to 40 GPa, 80 to 20 GPa and 8 to 1 GPa for imposed stress cycles at 828 °C, 892 °C and 918 °C, respectively. We theoretically estimate a tensile strength at failure of approximately 7–11 MPa, consistent with recent field data and in agreement with a model derived from the sample geometry and basic material parameters. Post-experimental neutron computed tomography and microscopic analyses further reveal the fragmentation of the melt and generation of tuffisite veins inside the conduit due to spontaneous crack nucleation associated with conduit wall fracture. The geometry of the rupture area inside the melt is akin to a Mach cone associated with supershear fractures. We discuss our findings in terms of magma-rock interaction leading to dykes, tuffisite veins and magma fragmentation.