The present work is devoted to fill the lack of data related to the hydrogen behavior in the vicinity of monovacancy in the hexagonal compact structure of beryllium. These data are of importance to feed coupled reaction–diffusion models dedicated to the simulation of hydrogen behavior in beryllium in order to analyze its thermal release as function of concentration and temperature. This work aims to evaluate the trapping and detrapping energies for several pathways surrounding a vacancy as well as the impact of multiple trapping of hydrogen on these data. In addition, the data to compute the detrapping rates for a single hydrogen are given. The determination of the energy landscape in the vicinity of the monovacancy has shown that the trapping energy varies from 0.39 eV (equal to the activation energy for diffusion in non-defective bulk) down to 0.12 eV while the activation energy for detrapping mechanism rises to 1.08 eV up to 1.48 eV. The lowest detrapping energy, 0.86 eV, is obtained from hydrogen filled vacancy whereas the multi-trapping does not significantly affect the trapping energy.