We employed the new issue of a parton and hadron cascade model PACIAE 2.1 to systematically investigate the charged particle elliptic flow parameter $v_2$ in the relativistic nuclear collisions at RHIC and LHC energies. With randomly sampling the transverse momentum $x$ and $y$ components of the particles generated in string fragmentation on the circumference of an ellipse instead of circle originally, the calculated charged particle $v_2(\eta)$ and $v_2(p_T)$ fairly reproduce the corresponding experimental data in the Au+Au/Pb+Pb collisions at $\sqrt{s_{NN}}$=0.2/2.76 TeV. In addition, the charged particle $v_2(\eta)$ and $v_2(p_T)$ in the p+p collisions at $\sqrt s$=7 TeV as well as in the p+Au/p+Pb collisions at $\sqrt{s_{NN}}$=0.2/5.02 TeV are predicted. Comment: 7 pages, 5 figures
