The non-ideal collective and plasma screening effects on elastic electron-atom collisions are investigated in partially ionized hydrogen plasmas using the first-order eikonal method. The effective pseudopotential model, taking into account the screening and collective effects, is applied to describe the interaction potential in non-ideal plasmas. Semiclassical trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase and cross section as functions of the impact parameter, the non-ideality plasma parameter, the Debye length, and the collision energy. The results show that the collective and screening effects enhance the differential eikonal cross section for small impact parameters, but suppress the cross section for large impact parameters. It is also found that the non-ideal collective effects enhance the total eikonal cross section.