Shear thinning and brittle failure of silicate melt control the dynamics of volcanic eruptions, but their molecular‐scale origin is still unclear. Here, we conducted tension and compression experiments on silicate melts, using time‐resolved X‐ray diffraction. Our experiments revealed that the intermediate‐range ordering of silicate structures, that is, the ring size formed by the SiO4 tetrahedra, demonstrated elastic and anisotropic dilation under tension and shrinkage under compression in the non‐Newtonian regime. In contrast, there were no significant changes in short‐range ordering, such as Si–O and Si–Si distances. Based on these findings, we inferred that shear thinning observed under high stress originates from the formation of anisotropically deformed large and small rings in silicate structures that are energetically unfavorable and unstable. Brittle failure occurred under high‐stress conditions, in both tension and compression. We propose a stress criterion as a necessary and sufficient condition for magma failure, rather than a strain rate criterion.