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Summary This paper presents a shake‐table test study to investigate the displacement capacity of shear‐dominated reinforced masonry wall systems and the influence of wall flanges and planar walls perpendicular to the direction of shaking (out‐of‐plane walls) on the seismic performance of a wall system. Two full‐scale, single‐story, fully grouted, reinforced masonry wall specimens were tested to the verge of collapse. Each specimen had two T‐walls as the seismic force‐resisting elements and a stiff roof diaphragm. The second specimen had six additional planar walls perpendicular to the direction of shaking. The two specimens reached maximum roof drift ratios of 17% and 13%, without collapsing. The high displacement capacities can be largely attributed to the presence of wall flanges and, for the second specimen, also the out‐of‐plane walls, which provided an alternative load path to carry the gravity load when the webs of the T‐walls had been severely damaged. The second specimen developed a higher lateral resistance than the first owing to the additional axial compression exerted on the T‐walls by the out‐of‐plane walls when the former rocked. The shear resistance of the T‐walls evaluated with the design code formula matches the test result well when this additional axial compression is taken into account. However, it must be understood that the beneficial influence of the wall flanges depends on the magnitude of the gravity load because of the P‐Δ effect and the severity of damage induced in the wall flanges when the wall system is subjected to bidirectional ground motions.