  In this paper, we study the metric dimension problem in maximal outerplanar
graphs. Concretely, if $\beta (G)$ is the metric dimension of a maximal
outerplanar graph $G$ of order $n$, we prove that $2\le \beta (G) \le \lceil
\frac{2n}{5}\rceil$ and that the bounds are tight. We also provide linear
algorithms to decide whether the metric dimension of $G$ is 2 and to build a
resolving set of size $\lceil \frac{2n}{5}\rceil$ for $G$. Moreover, we
characterize the maximal outerplanar graphs with metric dimension 2.
