Let G be a connected real Lie group and \(\Gamma\) a closed subgroup of G. Then \(\Gamma\) is called a lattice if G/\(\Gamma\) is compact. Every basis of the Lie algebra \({\mathfrak g}\) of G determines a parallelization of G/\(\Gamma\) and hence by the Thom-Pontryagin construction an element [G/\(\Gamma\) ], the stable homotopy of spheres. Earlier by one of the authors it was shown that for nilpotent groups G the d-invariant of [G/\(\Gamma\) ] vanishes except in dimensions one and two. In the article this result is extended to solvmanifolds. It is proved the following basic Theorem. Let G be a simply connected solvable Lie group of dimension \(m>2\) where \(m=1,2 mod 8\). Then for any lattice \(\Gamma\) in G we have \(d[G/\Gamma]=0\).