Molecular dynamics simulations are used to investigate the behaviour of D atoms at two interfaces between Beryllium (Be) and Beryllium oxide (BeO). After relaxation of the simulation cell, there are (i) localised defects at the interface and (ii) a hexagonal misfit dislocation network creating a succession of compressed and expanded area from each side of the interface. The simulations between 750 K and 1500 K for tens to hundreds of nanoseconds show that both interfaces act as trapping sites for D atoms. The simulations also show that D atoms tend to migrate in the material where the H solubility is the highest as predicted by thermodynamics. However, the simulations also shows that there are additional kinetic barriers (D trapping sites, D2 formation/dissociation in BeO) that slow down the path to equilibrium. These additional kinetic barriers may influence the fuel retention and permeation in Be materials.