We investigate the thermal stresses for GaAs layers grown on V-groove patterned Si substrates by the finite-element method. The results show that the thermal stress distribution near the interface in a patterned substrate is nonuniform, which is far different from that in a planar substrate. Comparing with the planar substrate, the thermal stress is significantly reduced for the GaAs layer on the patterned substrate. The effects of the width of the V-groove, the thickness, and the width of the SiO₂ mask on the thermal stress are studied. It is found that the SiO₂ mask and V-groove play a crucial role in the stress of the GaAs layer on Si substrate. The results indicate that when the width of V-groove is 50 nm, the width and the thickness of the SiO₂ mask are both 100 nm, the GaAs layer is subjected to the minimum stress. Furthermore, Comparing with the planar substrate, the average stress of the GaAs epitaxial layer in the growth window region of the patterned substrate is reduced by 90%. These findings are useful in the optimal designing of growing high-quality GaAs films on patterned Si substrates.