Particulate debris beds may form during different stages of a severe core melt accident; e.g. in the degrading hot core, due to thermal stresses during reflooding, in the lower plenum, by melt flow from the core into water in the lower head, and in the cavity by melt flow out of a failing RPV into a wet cavity. Deep water pools in the cavity are used in Nordic BWRs as an accident management measure aiming at particulate debris formation and coolability. It has been elaborated in the joint work of the European Severe Accident Research Network (SARNET) in Work Package (WP) 11.1 that coolability of particulate debris, reflooding of hot debris as well as boil-off under decay heat (long-term coolability), is strongly favoured by 2D/3D effects in beds with non-homogeneous structure and shape. Especially, water inflow from the sides and via bottom regions strongly improves coolability as compared to 1D situations with top flooding, the latter being in the past the basis of analyses on coolability. Data from experiments included in the SARNET network (DEBRIS at IKE and STYX at VTT) and earlier ones (e.g. POMECO at KTH) have been used to validate key constitutive laws in 2D codes as WABE (IKE) and ICARE/CATHARE (IRSN), especially concerning flow friction and heat transfer. Major questions concern the need of the explicit use of interfacial friction to adequately treat the various flow situations in a unified approach, as well as the adequate characterization of realistic debris composed of irregularly shaped particles of different sizes. Joint work has been supported by transfer of the WABE code to KTH and VTT. Concerning realistic debris, the formation from breakup of melt jets in water is investigated in the DEFOR experiments at KTH. Present results indicate that porosities in the debris might be much higher than previously assumed, which would strongly support attainment of coolability. Calculations have been performed with IKEJET/IKEMIX describing jet breakup, mixing and settling of resulting particles. Models about debris bed formation and porosity are developed at KTH. The codes have been applied to reactor conditions for analysing the potential for coolability in the different phases of a severe accident. Calculations have been performed with WABE (MEWA) implemented in ATHLET-CD and with ICARE/ICATHARE for degraded cores and debris beds in the lower plenum, under reflooding and boil-off. Ex-vessel situations have also been analysed. Strong effects of lateral water inflow and cooling by steam in hot areas have been demonstrated. In support, some typical basic configurations have been analysed, e.g. configurations with downcomers considered as possible AM measures. Melt pool formation or coolability of particulate debris is a major issue concerning melt retention in the core and the lower head. Present conclusions from those analyses for adequate modelling in ASTEC are outlined as well as remaining uncertainties. Experimental and analysis efforts and respective continued joint actions are discussed, which are needed to reach resolution of the coolability issue.