The etiology of persistent stuttering is unknown, but stuttering has been attributed to multiple potential factors, including difficulty in processing language-related information, but findings remain inconclusive regarding any specific linguistic deficit potentially causing stuttering. One particular challenge in drawing conclusions is the highly variable task demands across studies. Different tasks could potentially reflect either different processes, or different levels of demand. This study examined the role of cognitive demand in semantic and phonological processes to evaluate the role of linguistic processing in the etiology of stuttering. The study examined concurrent processing of picture naming and tone-identification in typically fluent young adults, adults who stutter (AWS) and matched adults who do not stutter (NS), with varying temporal overlap between the dual tasks as manipulation of cognitive demand. The study found 1) that in both AWS and NS, semantic and phonological encoding both interacted with non-linguistic processing during concurrent processing, suggesting that both linguistic processes are demanding in cognitive resources, 2) that there was no observable relationship between dual-task interference to word encoding and stuttering, 3) that AWS and NS showed different trends of phonological encoding under high but not low cognitive demand, suggesting a subtle phonological deficit in AWS, and 4) that the phonological encoding effect correlated with stuttering rate, suggesting that phonological deficit could potentially play a role in the etiology or persistence of stuttering. Additional findings include potential differences in semantic encoding between typically fluent young adults and middle-age adults, as well as potential strategic differences in processing semantic information between AWS and NS. Findings were taken to support stuttering theories suggesting specific deficits in phonological encoding and argue against a primary role of semantic encoding deficiency or lexical access deficit in stuttering.