Band calculations show that a stripelike antiferromagnetic spin wave is enforced by a ‘‘half-breathing'' phonon distortion within the CuO plane of HgBa2CuO4. This spin-phonon coupling is increased further by shear distortion and by the increased distance between Cu and apical oxygens. The effects from spin-phonon coupling are consistent with many observations in high-Tc materials. Spin-phonon coupling can be important for the mechanism of spin fluctuations and superconductivity, although the effects are quantitatively weak when using the local density potential.