International audienceContext: Rigorous modeling of the Ba II lambda4554 formation is potentially interesting since this strongly polarized line forms in the solar chromosphere where the magnetic field is not very well known. Aims: We investigate the role of isotropic collisions with neutral hydrogen in the formation of the polarized Ba II lambda4554 line and, thus, in the determination of the magnetic field. Methods: Multipole relaxation and transfer rates of the d- and p-states of Ba II by isotropic collisions with neutral hydrogen are calculated. We consider a plane-parallel layer of Ba II that is situated at the low chromosphere and that is anisotropically illuminated from below, which produces linear polarization in the lambda4554 line...