When grown in a substrate subjected to cyclic stretching, most types of cells change orientations. This cell orientation response (COR) has been shown to be driven by axial substrate strain (the strain beneath and along a cell's long axis). However, it remains unclear whether COR depends on the strain direction (tension vs compression). Furthermore, in vitro COR is paradoxical, since in vivo fibroblasts align along collagen fibers and hence the stretch direction. We hypothesized that COR does not depend on the surface strain direction, and that contact guidance provided by microgrooves can maintain cell alignment in the presence of cyclic stretching. Human skin fibroblasts were cultured on compliant smooth and microgrooved surfaces in silicone dishes. Cyclic uniaxial tensile and compressive strains (4%, 8% and 12%) were applied on the dishes at 1 Hz for 24 h. Cell orientation distributions were determined and compared using the Kolmogorov-Smirnov test. Significant differences were found between each of cell orientation distributions with the applied strains and that without strains (p < 0.05). Nevertheless, no significant differences were found between two cell orientation distributions for each pair of opposite strains applied (for 4%, p = 0.33; for 8%, p = 0.18; and for 12%, p = 0.32). Moreover, fibroblasts grown in microgrooves aligned in the groove direction and remained so after 8% cyclic stretch. Thus, this study showed that COR is the cells' avoidance to substrate deformation (i.e., strain-direction independent). It also suggested that the failure of fibroblasts to change orientations in vivo may result from the contact guidance provided by collagen fibers.