Using the projector-augmented wave method within the generalized gradient approximation, a systematic first-principles calculation for energy vs. volume (E-V) equations of state (EOS's) and single crystal elastic stiffness constants (c(ij)'s) has been performed for 76 pure elemental solids with face-centered-cubic (fcc), body-centered-cubic (bcc), and hexagonal-close-packed (hcp) crystal structures, wherein the c(ij)'s are determined by an efficient strain-stress method, and the EOS's are fitted by a 4-parameter Birch-Murnaghan equation upon the first-principles E-V data points. Based on the predicted EOS's and c(ij)'s, the phase transition pressures between bcc, fcc, and hcp structures, as well as the structural stabilities and the polycrystalline aggregate properties including bulk modulus (B), shear modulus (G), B/G ratio, and anisotropy ratio have been analyzed for pure elements and compared with available experimental data. The present systematic studies of pure elements provide not only the EOS's and c(ij)'s but also the benchmarks of first-principles calculations. (C) 2010 Elsevier B.V. All rights reserved.