  A new formalism is used for a Monte Carlo determination of the elastic
constants of a two-dimensional net of fixed connectivity. The net is composed
of point-like atoms each of which is tethered to six neighbors by a bond
limiting the distance between them to a certain maximal separation, but having
zero energy at all smaller lengths. We measure the elastic constants for many
values of the ratio $\gamma$ between the maximal and actual extensions of the
net. When the net is very stretched ($\gamma\sim 1$), a simple transformation
maps the system into a triangular hard disks solid, and we show that the
elastic properties of both systems, coincide. We also show that the crossover
to a Gaussian elastic behavior, expected for the non-stressed net, occurs when
the net is more loose ($\gamma\sim 3$).
