The authors report a new theory of false memory building upon existing associative memory models and implemented in fSAM, the first fully specified quantitative model of false recall. Participants frequently intrude unstudied critical words while recalling lists comprising their strongest semantic associates but infrequently produce other extralist and prior-list intrusions. The authors developed the theory by simulating recall of such lists, using factorial combinations of semantic mechanisms operating at encoding, retrieval, or both stages. During encoding, unstudied words' associations to list context were strengthened in proportion to their strength of semantic association either to each studied word or to all co-rehearsed words. During retrieval, words received preference in proportion to their strength of semantic association to the most recently recalled single word or multiple words. The authors simulated all intrusion types and veridical recall for lists varying in semantic association strength among studied and critical words from the same and different lists. Multiplicative semantic encoding and retrieval mechanisms performed well in combination. Using such combined mechanisms, the authors also simulated several core findings from the Deese-Roediger-McDermott paradigm literature, including developmental patterns, specific list effects, association strength effects, and true-false correlations. These results challenge existing false-memory theories.