Cyclically stretched cells are known to exhibit a strain-induced reorientation response. In this study, we comprehensively analyse this behaviour for human fibroblasts subjected to a highly non-uniform strain field within a polymethylsiloxane microdevice. We demonstrate a strong correlation between the strain amplitude and the degree of cell alignment perpendicular to the principal strain direction (stretching avoidance). Analogously, our results indicate that the strain gradient amplitude and direction also regulate this reorientation through a coordinated gradient avoidance response. We stipulate that strain gradients are thus biologically relevant mechanical cues sensed by cells. To gain insight into the underlying mechanosensing processes, we also studied focal adhesion reorganization and the effect of modulating myosin-II contractility. The extracted focal adhesion orientation distributions are similar to those obtained for the cell bodies, and their density is increased by the presence of stretching forces. Moreover, it was found that the myosin-II activity promoter calyculin-A has little effect on the cellular response, while the inhibitor blebbistatin suppresses cell and focal adhesion alignment and reduces focal adhesion density. These results confirm that similar internal structures involved in sensing and responding to strain direction and amplitude are also key players in strain gradient mechanosensing and avoidance.