The two-dimensional optimal velocity model has potential applications to pedestrian dynamics and the collective motion of animals. In this paper, we extend the linear stability analysis presented in a previous paper [A Nakayama, Phys. Rev. E. 77, 016105 (2008)10.1103/PhysRevE.77.016105] and investigate the effects of particle configuration on the stability of several wave modes of collective oscillations of moving particles. We find that, when a particle moves without interacting with particles that are positioned in a diagonally forward or backward direction, the stable region of the particle flow is completely removed by the elliptically polarized mode.