Methods are described for the production of soybean varieties and lines exhibiting linolenic acid contents of less than about 2.5% of the total fatty acid composition as determined by gas chromatography, preferably less than about 2.2% and, more preferably, less than about 1.9%, and in one aspect of the invention, soybean varieties and lines having the low linolenic acid characteristic and a stearic acid content of at least 20%, preferably at least 25%, and, more preferably, at least about 30%, and in a further aspect, soybean varieties and lines having the low linolenic acid content and a palmitic acid content of at least 11%, more preferably at least about 13 or 14%. In accordance with still further aspects of this invention, soybean lines are provided which exhibit a low linolenic acid content and an oleic acid content of at least about 60% of the total fatty acid composition, such lines may, if desired, also contain a palmitic acid content of less than about 6.0% and/or a stearic acid content of less than about 3.5%. There is also disclosed soybean lines having low linolenic acid contents and a palmitic acid content of less than about 5.0%, preferably less than about 4.0%.