The bremsstrahlung flux-averaged cross-sections 〈σ(E
γmax)〉 and the cross-sections per equivalent photon 〈σ(E
γmax)Q〉 were first measured for the photonuclear multichannel reaction 27Al(γ,x)22Na at end-point bremsstrahlung gamma energies ranging from 35 MeV to 95 MeV. The experiments were performed with 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 GEANT4.9.2 and, in addition, was monitored by means of the 100Mo(γ,n)99Mo reaction. The flux-averaged cross-sections were calculated using the partial cross-section σ(E) values computed with the TALYS1.95 code for different level density models. Consideration is given to special features of calculating the cross-sections 〈σ(E
γmax)〉 and 〈σ(E
γmax)Q〉 for the case of the final nucleus 22Na via several partial channels x: nα + dt + npt + 2n3He + n2d + 2npd + 2p3n.