The paper discusses different modelling assumptions for spandrels in equivalent frame models and their effect on the global response of the wall. The topic is motivated by the following issues: i) reliable and practice oriented numerical tools constitute a key instrument to support mitigation policies and plan effective (in terms of cost and impact) retrofit interventions; ii) spandrels have lately been increasingly recognized to play a significant role on the load bearing capacity of masonry walls; iii) despite the experimental evidence of last years that highlighted significant differences between spandrels and piers, numerical tools available in literature and recommendations of codes do not yet account properly for the progress achieved with regard to spandrel models. To deepen such issues, various strength criteria specifically formulated for spandrels and available in literature have been implemented in the Tremuri program, including those proposed by Beyer (2012) that have been recently incorporated in the updated release of the NZSEE recommendations. With the so enhanced program, parametric nonlinear static analyses on 2D masonry walls have been performed to quantitatively assess the influence of spandrel modelling.