The three-dimensional non-linear earthquake behaviour of unreinforced masonry buildings is studied by using a constitutive model established experimentally for burned-clay brick masonry wall panels. The parameter functions appearing in the constitutive model are modified so that they accommodate a wall panel made of a general masonry material. In the study it is assumed that the floors of the masonry building are reinforced concrete slabs which are infinitely rigid in their own planes and that the wall panels possess only in-plane rigidities. Some examples involving earthquake analyses of two different masonry structures are presented. It is found that the predictions of the model used in the study are in harmony with the experimental data available in the literature.