  Let $U_{FNA}$ be the class of all non-archimedean finite-dimensional Banach
spaces. A non-archimedean Gurarii Banach space $G$ over a non-archimedean
valued field $K$ is constructed, i.e. a non-archimedean Banach space $G$ of
countable type which is of almost universal disposition for the class
$U_{FNA}$. This means: for every isometry $g : X \to Y$ , where $Y \in U_{FNA}$
and $X$ is a subspace of $G$, and every $\varepsilon \in (0,1)$ there exists an
$\varepsilon$-isometry $f : Y \to G$ such that $f(g(x)) = x$ for all $x \in X$.
We show that all non-archimedean Banach spaces of almost universal disposition
for the class $U_{FNA}$ are $\varepsilon$-isometric. Furthermore, all
non-archimedean Banach spaces of almost universal disposition for the class
$U_{FNA}$ are isometrically isomorphic if and only if $K$ is spherically
complete and $\{|\lambda| : \lambda \in K \setminus \{0\} \} = (0,\infty)$.

Functional Analysis