  In this paper, we give a complete classification of harmonic and biharmonic
Riemannian submersions $\pi:(R^3,g_{Sol})\to (N^2,h)$ from Sol space into a
surface by proving that there is neither harmonic nor biharmonic Riemannian
submersion $\pi:(R^3,g_{Sol})\to (N^2,h)$ from Sol space no matter what the
base space $(N^2,h)$ is. We also prove that a Riemannian submersion
$\pi:(R,g_{Sol})\to (N^2,h)$ from Sol space exists only when the base space is
a hyperbolic space form.
