This work illustrates a theoretical model developed to reproduce the behaviour of ancient masonry subjected to sustained stresses. Starting from a model recently proposed by the authors, two damage tensors have been introduced into a rheological model: the components of these tensors change both according to the intensity of the applied stress and, in case of sustained stress, to the duration of the load history. Evolution laws found in the literature for brittle materials have been employed. The principal directions of damage are meant to represent the directions of the experimental cracks; accordingly, when any damage direction is activated, it remains unchanged throughout the subsequent load history. The presence of second-order damage tensors makes it possible to describe the damage-induced anisotropy of the microcracked material. Also, since the possible increase of damage in time is accounted for, the model is able to describe creep failure and to predict the creep time to failure of the material under given stresses. The model parameters can be obtained through uniaxial creep tests on masonry samples at increasing stress levels and up to failure. The model was implemented into a finite element code, and structural analyses were carried out to assess the safety of middle-age masonry towers. The results obtained for one of these towers are briefly described and discussed.