Soybean [Glycine max (L.) Merr.] cultivars with increased levels of palmitic or stearic acid in the seed oil could reduce the need for chemical modifications during processing for some vegetable oil products. Mutants with altered levels of the fatty acids were developed by artificial mutagenesis with ethyl methane sulfonate (EMS). Four of the mutants had 128 to 182 g kg−1 palmitic acid compared with 90 to 100 g kg−1 in their parents, and four mutants had 132 to 301 g kg−1 stearic acid compared with 33 to 51 g kg−1 in their parents. The objective of this study was to determine the inheritance of palmitic or stearic acid in the seed oil of the eight mutants. Reciprocal crosses were made between each mutant and the cultivar Coles, among three of the palmitic mutants, and between the high‐stearic acid line A6 and the four stearic mutants. Fatty acid analysis of the parents and F1, F2, and F3 generations indicated that the allele controlling low palmitic and low stearic acid in Coles exhibited partial dominance to the alleles in PA1, PA2, PA3, ST1, ST2, ST3, and ST4 and no dominance to the allele in PA4. The crosses between A6 and the stearic mutants indicated that the alleles controlling high stearic acid in ST1, ST3, and ST4 occurred at the same locus as the fasa allele in A6 and that the allele in ST2 may occur at a different locus. Significant maternal and cytoplasmic effects on palmitic and stearic acid content were not confirmed in any of the mutants.