We study the formation of the lunar wake by a quasi-neutral hybrid (QNH) model. In the model ions are particles while electrons form a massless change neutralizing fluid. The model is three dimensional enabling us to study non-axisymmetric filling of the tail with solar wind plasma resulting from non-axisymmetric electromagnetic forces. We find that already a not fully kinetic QNH model can reproduce some of the basic observed features, namely (1) a long (over 10 lunar radii) tail of depleted plasma density, (2) enhanced magnetic field within the optical shadow and depressed magnetic field near the edge of the optical shadow and (3) non-Maxwellian plasma beams with high temperature anisotropy. The analysis also supports previous studies which have emphasized the role of the direction of the magnetic field and kinetic effects in the lunar wake.