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In the homogeneous space Sol${}_3$, a translation surface is parametrized by $r(s,t)={\gamma }_1\left(s\right)*{\gamma }_2\left(t\right)$, where ${\gamma }_1$ and ${\gamma }_2$ are curves contained in coordinate planes. In this article, we study translation invariant surfaces in ${\mathrm{Sol}}_3$, which has finite type immersion.