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BACKGROUND The significance of high‐molecular‐weight glutenin subunits (HMW‐GSs) and rye translocations, and their associations with gluten strength for hard wheat used for making bread has been understood well, but remains poorly understood for soft wheat used for making cookies. The influences of HMW‐GSs and rye translocations on the dough‐mixing properties and cookie‐baking quality of soft wheat were investigated using 50 US eastern soft winter (ESW) wheat varieties possessing 14 predominant HMW‐GS profiles. RESULTS: Glu‐A1 and Glu‐B1 loci only influenced dough‐mixing properties significantly, whereas the Glu‐D1 locus influenced both dough‐mixing properties and cookie‐baking quality significantly. The subunits 1, 7* + 8 and 5 + 10 at the Glu‐A1, Glu‐B1 and Glu‐D1 loci, respectively, were associated with a long midline peak time, whereas only the rare subunits 2 + 121 at the Glu‐D1 locus exhibited significant associations with improved cookie‐baking quality of ESW wheat. The contributions of rye translocations to dough‐mixing properties and cookie‐baking quality depended on HMW‐GS profiles. Three HMW‐GS profiles (2*, 7 + 9, 2 + 121), (2*, 7 + 8, 2 + 121) and (1, 7 + 8, 2 + 121) were identified as being desirable for making large‐diameter cookies. Flour protein content, lactic acid (LA), and sodium carbonate (SC) solvent retention capacities and softness equivalence were identified as effective predictors of cookie diameter and accounted for 79% of the variation in cookie diameter. CONCLUSION: Subunits 2 + 121 have significant associations with the protein characteristics and cookie‐baking quality of soft wheat. The determination of HMW‐GS composition would be an effective tool in soft‐wheat breeding programs for quickly identifying and selecting acceptable breeding lines possessing desirable cookie‐baking potential. Published 2020. This article is a U.S. Government work and is in the public domain in the USA. [ABSTRACT FROM AUTHOR]