That mechanical properties of the extracellular environment can influence cell behaviour has already been established. Recent studies indicate that human mesenchymal stem cells are affected by the surface curvature of the underlying substrate. However, how meso-scale substrate curvature affects cell behaviour is still not clear. This study utilised the finite element method to simulate a prestressed human mesenchymal stem cell conforming and attaching to a flat control substrate, concave hemispherical and concave cylindrical substrates with curvature radii from 300 µm to 75 µm. The cell model comprises the actin cortex, cytoskeleton, and nucleus modelled with a hyperelastic material definition and 30 linear elastic stress fibres prestressed with a force of 10 nN. The effects of surface curvature on cellular traction forces, cell height, nuclear aspect ratio and actin cortex was studied. The vertical traction forces were observed to be 70% and 40% lower for the hemispherical and cylindrical substrates of the highest curvatures compared to the flat control substrate, respectively. Cellular traction forces towards the cell periphery were roughly 10-20% higher than the more central cellular traction forces independent of substrate curvature. Stresses in the actin cortex were observed to increase by 290% and 220% from the flat control substrate to the hemispherical and cylindrical substrates of the highest curvatures, respectively. These results indicate that the cell is more sensitive to hemispherical substrates than cylindrical substrates. The results also support in vitro observations where hMSCs are seen to span hemispherical substrates and avoid continuous contact.