Using the density functional theory, formulated within the framework of the exact muffin-tin orbitals method, we have calculated the surface stress for the $(111)$ free surfaces of the fcc $4d$ and $5d$ transition metals. Good agreement is obtained with the available ab initio data for Pd, Ir, and Au, while for Pt we predict a surface stress, which is about 33% lower compared to former theoretical results. The present surface stress values for the $4d$ and $5d$ fcc metals show the typical trend characteristic for the cohesive or surface energies of d series.