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The prototype model of a fluidized granular system is a gas of inelastic hardspheres (IHS) with a constant coefficient of normal restitution $\alpha$. Usinga kinetic theory description we investigate the two basic ingredients that amodel of elastic hard spheres (EHS) must have in order to mimic the mostrelevant transport properties of the underlying IHS gas. First, the EHS gas isassumed to be subject to the action of an effective drag force with a frictionconstant equal to half the cooling rate of the IHS gas, the latter beingevaluated in the local equilibrium approximation for simplicity. Second, thecollision rate of the EHS gas is reduced by a factor $(1+\alpha)/2$, relativeto that of the IHS gas. Comparison between the respective Navier-Stokestransport coefficients shows that the EHS model reproduces almost perfectly theself-diffusion coefficient and reasonably well the two transport coefficientsdefining the heat flux, the shear viscosity being reproduced within a deviationless than 14% (for $\alpha\geq 0.5$). Moreover, the EHS model is seen to agreewith the fundamental collision integrals of inelastic mixtures and dense gases.The approximate equivalence between IHS and EHS is used to propose kineticmodels for inelastic collisions as simple extensions of known kinetic modelsfor elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for  publication in PR

System of elastic hard spheres which mimics the transport properties of a granular gas