By means of particle dynamics simulations, we investigate the elastic moduli of dense packings of spherical and dodecahedral monodisperse particles. The samples are prepared by isotropic compaction under constant load and zero friction, leading to the densest isotropic state, which is unique for each particle type. Then, they are subjected to quasi-static triaxial compression using tri-periodic boundary conditions, thereby removing spurious wall effects, for different values of the interparticle friction coefficient (from 0.1 to 0.4). From the stress and strain data, we evaluate the effective elastic moduli (the Young modulus, bulk modulus and Poisson ratio) at several instances of deformation by applying shear reversal. We find that the elastic moduli are independent of the friction coefficient at very small shear deformations due to the stability of the contact network at such dense states, but undergo considerable change at larger deformations when interparticle contacts begin to slide or are lost along the direction of extension. Notably, beyond this point the Young modulus declines with further deformation to a value all the more small that the friction co- efficient is larger. In all cases, the bulk modulus increases with deformation. The shear modulus is found to be larger for polyhedral particles due to stronger constraints on particle movements. Our data show that the initial Poisson ratio is 0.12 for spherical particle packings, in agreement with those of Agnolin and Roux [1], and 0.09 for packings of rigid polyhedral particles. This lower value of the Poisson ratio reflects the lower mobility of the particles.