A theoretical analysis using three well-known masonry analysis constitutive models is performed on a masonry structure to simulate the response of the structure to specific seismic forces. The results of the three numerical approaches are compared and a discussion is presented, mainly intended for professionals, concerning the suitability of the three models and the limitations of each numerical approach. The aim of the study is to evaluate the relative accuracy of the three different models and their suitability for determining the failure mode of the masonry chimney. The models studied are: a linear elastic constitutive model, an elastic-plastic Drucker-Prager’s type model and a model including cracking and/or crushing in the material using Willam-Warnke’s criterion. A macromodelling approach is used because of the great number of elements forming the structure and the computational demand. Seismic actions are synthetically generated and scaled until chimney failure, in accordance with the present regulations on seismic-proof constructions in Europe and Spain. Conclusions for researchers and professionals are obtained to determine the suitability of each model according to the results required and the available calculation capacity.