  We construct classes in the middle degree plus one motivic cohomology of the
Siegel Shimura variety of almost any dimension. We compute their image by
Beilinson's higher regulator in terms of Rankin-Selberg type automorphic
integrals. Our construction generalises the one for $\mathrm{GSp}(4)$ and for
$\mathrm{GSp}(6)$. For Siegel varieties associated to small genus symplectic
groups, we also show how these integrals unfold.
