The bremsstrahlung flux-averaged cross-sections σ(E γmax ) and the crosssections per equivalent photon σ(E γmax ) Q were measured for the photonuclear multiparticle reaction 27 Al(γ, x; x = 3 He+pd+2pn) 24 Na at bremsstrahlung end-point energies ranging from 40 MeV to 95 MeV. The experiments were performed using the beam from the NSC KIPT electron linear accelerator LUE-40 with the use of the γ-activation technique. The bremsstrahlung quantum flux was calculated with the program GEANT4 and, in addition, was monitored by means of the 100 Mo(γ, n) 99 Mo reaction. The cross-sections σ(E) were computed using the TALYS1.9 code with the default options. The measured average cross-sections σ(E γmax ) and σ(E γmax ) Q have appeared to be higher by factors of 2.0 to 2.4 than the theoretical results. The experimental results have been found to be in good agreement with the data of other laboratories. Consideration is given to special features of calculation of σ(E γmax ) and σ(E γmax ) Q for the 27 Al(γ, x) 24 Na reaction, with occurrence of three 27 Al photodisintegration channels. The paper also discusses the possibility of using the 27 Al(γ, x) 24 Na reaction for monitoring the bremsstrahlung γ-quantum flux in the photon energy region above 30 MeV.