We study the macroscopic elastic moduli of an elastic percolating network in the critical region. A microscopic elastic Hamiltonian is used, which contains a bending energy term. We find that the rigidity threshold of this system is identical to the percolation threshold pc. By considering the elastic properties of elements of the infinite percolation cluster we calculate the critical exponent which describes the behavior of the elastic stiffness near pc for d=6 and obtain a lower bound on for d<6. is considerably higher than the conductivity exponent t, suggesting that the elastic problem belongs to a different universality class.