Through mechanotransduction, cells can sense physical cues from the extracellular environment and convert them into internal signals that affect various cellular functions. For example, human mesenchymal stem cells (hMSCs) cultured on topographical gratings have been shown to elongate and differentiate to different extents depending on grating width. Using a combination of experiments and mathematical modeling, the physical parameters of substrate topography that direct cell elongation were determined. On a variety of topographical gratings with different grating widths, heights and rigidity, elongation of hMSCs was measured and a monotonic increase was observed for grating aspect ratio (crosssectional height to line-width ratio) between 0.035 and 2. The elongation was also dependent on the grating substrate rigidity over a range of 0.18-1.43 MPa. A mathematical model was developed to explain our observations by relating cell elongation to the anisotropic deformation of the gratings and how this anisotropy depends on the aspect ratio and rigidity of the gratings. Our model was in good agreement with the experimental data for the range of grating aspect ratio and substrate rigidity studied. In addition, we also showed that the percentage of aligned cells, which had a strong linear correlation with elongation for slightly elongated cells, saturated toward 100 % at higher level of cell elongation. Our results may be useful in designing gratings to elicit specific cellular responses that may depend on the extent of cell elongation.