  In this paper we generalize in Lorentz-Minkowski space $\l^3$ the
two-dimensional analogue of the catenary of Euclidean space. We solve the
Dirichlet problem for bounded mean convex domains and spacelike boundary data
that have a spacelike extension to the domain. We also classify all singular
maximal surfaces of $\l^3$ invariant by a uniparametric group of translations
and rotations.
