The hyperfine structures of ^7,9Be⁻  2s2p^2  4P _1/2,3/2,5/2 are investigated theoretically using the multiconfiguration Hartree–Fock and configuration interaction methods. The effects of the hyperfine mixing between the fine-structure J-levels are discussed. The feasibility of some atomic spectroscopy experiments, allowing determination of the ⁷Be quadrupole moment from the observed hyperfine structure of the ⁷Be⁻ negative ion and from the present electronic parameters, is investigated. The Be 2s2p ³P^o electron affinity is monitored as a function of the orbital and configuration spaces to assess the reliability of the wavefunctions of the neutral atom and the negative ion. The theoretical value nicely converges towards the most recent theoretical and experimental results.