Entrainment into the stratocumulus-topped boundary layer (STBL) is investigated by means of large-eddy simulations. Set-up of the numerical experiment is based on the research flight RF-01 in the DYCOMS-II field campaign. We focus on the stability of the flow in the cloud-top region known as the Entrainment Interface Layer (EIL). We calculate the local gradient Richardson number, Ri, at the surface of maximum static stability and at the material top of the STBL defined by a threshold of the total water content. We found that regions in which updraughts impinge upon the inversion and diverge horizontally are characterized by small values of Ri. Resulting turbulence is responsible for entrainment and formation of the EIL. Volumes of the STBL air and the free-tropospheric air from above it, mixed in proportion resulting in negative buoyancy and typically void of cloud water, form 'cloud holes' - trenches of descending cloud-free air which surround updraught areas. The entrainment process is further analyzed using a passive scalar introduced after three hours of the simulation above the layer of maximum static stability. The mixing fraction of this scalar in the air within the cloud holes falls within the range corresponding to the buoyancy reversal. Some of the negatively buoyant mixtures sinking through the cloud holes are wrapped around the edge of cloudy regions and recirculated into the cloud, which causes a local increase of the cloud-base height. The rest of the entrained free-tropospheric air sinks slowly into the STBL and leads to its gradual dilution.