Wheat cultivars possessing quality attributes needed to produce optimum quality tortillas have not been identified. This study investigated the effect of variations in high‐molecular‐weight glutenin subunits encoded at the Glu‐1 loci (Glu‐A1, Glu‐B1, and Glu‐D1) on dough properties and tortilla quality. Flour protein profiles, dough texture, and tortilla physical quality attributes were evaluated. Deletion at Glu‐D1 resulted in reduced insoluble polymeric protein content of flour, reduced dough compression force, and large dough extensibility. These properties produced very large tortillas (181 mm diameter) compared with a control made with commercial tortilla wheat flour (161 mm). Presence of a 7 + 9 allelic pair at Glu‐B1 increased dough strength (largest compression force, reduced extensibility, and small‐diameter tortillas). Deletion at Glu‐A1 produced large tortillas (173 mm) but with unacceptable flexibility during storage (score <3.0 at day 16). In general, presence of 2* at Glu‐A1, in combination with 5 + 10 at Glu‐D1, produced small‐diameter tortillas that required large force to rupture (tough texture). Presence of 2 + 12 alleles instead of 5 + 10 at Glu‐D1 produced tortillas with a good compromise between diameter (>165 mm) and flexibility during storage (>3.0 at day 16). These allele combinations, along with deletion at Glu‐D1, show promise for tortilla wheat development.