We consider a deformable body that occupies a region D in the plane. In our model, the body's elasticity tensor H (x) is the restriction to D of a second-order mean-square continuous random field. Under translation, the expected value and the correlation tensor of the field H (x) do not change. Under action of an arbitrary element k of the orthogonal group O (2), they transform according to the reducible orthogonal representation k bar right arrow S-2 (S-2 (k)) of the above group. We find the spectral expansion of the correlation tensor R (x) of the elasticity field as well as the expansion of the field itself in terms of stochastic integrals with respect to a family of orthogonal scattered random measures.