The structural, electronic and elastic properties of Rb-As systems (RbAs in NaP, LiAs and AuCu structures, RbAs2 in the MgCu2 structure, Rb3As in Na3As, Cu3P and Li3Bi structures, and Rb5As4 in the A(5)B(4) structure) are investigated with the generalized gradient approximation in the frame of density functional theory. The lattice parameters, cohesive energies, formation energies, bulk moduli and the first derivatives of the bulk moduli (to fit Murnaghan's equation of state) of the considered structures are calculated and reasonable agreement is obtained. In addition, the phase transition pressures are also predicted. The electronic band structures, the partial densities of states corresponding to the band structures and the charge density distributions are presented and analysed. The second-order elastic constants based on the stress-strain method and other related quantities such as Young's modulus, the shear modulus, Poisson's ratio, sound velocities, the Debye temperature and shear anisotropy factors are also estimated.