Series expansions in powers of the concentration p for elastic and other susceptibilities of randomly diluted elastic networks have been generated for a bond-bending model on a honeycomb lattice up to 13th order, and for the central-force model on a triangular lattice up to 22nd order, in p. Critical exponents for both models and the critical threshold of the central-force problem have been estimated by Padé-approximant-analysis techniques. We obtain exponent estimates that are consistent with scaling relations and other calculations. For the bond-bending model, the effective splay elastic constant scales like L−φsp/ν with φsp=1.20±0.015. For central-force elastic percolation, we find β+γ=1.9±0.2 and ν=1.1±0.2.