  We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin
values $0,1,2,...,m, m\geq2$ and non zero external field, on a Cayley tree of
order $k$. In the case $k=2, m=2$, we describe translation-invariant ground
states for the SOS model with a translation-invariant external field. Some
periodic ground states for the SOS model with periodic external field are
described.
