  In this paper we consider affine iterated function systems in locally compact
non-Archimedean field $\mathbb{F}$. We establish the theory of singular value
composition in $\mathbb{F}$ and compute box and Hausdorff dimension of
self-affine set in $\mathbb{F}^n$, in generic sense, which is an analogy of
Falconer's result for real case. The result has the advantage that no
additional assumptions needed to be imposed on the norms of linear parts of
affine transformation while such norms are strictly less than $\frac{1}{2}$ for
real case, which benefits from the non-Archimedean metric on $\mathbb{F}$.
