The flux-averaged cross-sections 〈σ(E
γmax)〉 for the reactions 65Cu(γ,n)64Cu, 63Cu(γ,n)62Cu, 63Cu(γ,2n)61Cu and 63Cu(γ,3n)60Cu have been measured within the bremsstrahlung end-point energies E
γmax range of 35–94 MeV. The experiments were performed with the electron beam from the NSC KIPT linear accelerator LUE-40 with the use of the activation and off-line γ-ray spectrometric technique. Theoretical calculation of the flux-average cross-sections 〈σ(E
γmax)〉th was carried out using the cross-section σ(E) values from the TALYS1.95 code with the default options. It is shown that the experimental average cross-sections for the reactions 65Cu(γ,n)64Cu, 63Cu(γ,n)62Cu, 63Cu(γ,2n)61Cu are systematically higher than the theoretical estimates based on the TALYS1.95 code. The obtained 〈σ(E
γmax)〉 supplement the data of different laboratories for the (γ,n) and (γ,2n) reactions of 63Cu and 65Cu. For the reaction 63Cu(γ,3n)60Cu, the values of 〈σ(E
γmax)〉 were measured for the first time.