<p>This paper investigates the long-wave asymptotic behavior of three-dimensional Euler-Poisson system describing cold ion plasmas, both in the unmagnetized case and in the case with a uniform magnetic field. Through an appropriate scaling which balances the nonlinearity and dispersion, we derive two decoupled Kadomtsev-Petviashvili (KP)/Zakharov-Kuznetsov (ZK) equations from the original system. A rigorous justification of the long-wave approximation is given by establishing uniform estimates of the difference between the solutions of Euler-Poisson system and a suitable constructed approximation profile. It demonstrates that solutions of Euler-Poisson system in unmagnetic case are well approximated by the two-way waves from the corresponding KP-II type equations, while the solutions of the system with magnetic field are convergent to the counter directional waves of the ZK equations.</p>