The elastic properties of the low-temperature solid phase of a 1,2-distearoyl-sn-glycero-3-phophatidylcholine (DSPC) monolayer spread at the air-water and at the air-formamide interfaces are studied by propagating surface waves in two perpendicular directions. On formamide, we detect anisotropies of both the surface tension and of the DSPC film compression modulus above a surface pressure threshold pi(c) approximate to 7 mN/m, corresponding to the onset of a buckling instability of the solid film. Above the threshold, the 2D Poisson coefficient continuously decreases from 1 to 0.7, and the film is more compressible in the buckled direction than in the orthogonal one. For the same film on water, where no buckling occurs, no anisotropies are detected. This method also provides a reasonable value for the film surface viscosity.