The semantic fluency task has been used to understand the ef-fects of semantic relationships on human memory search. Avariety of computational models have been proposed that ex-plain human behavioral data, yet it remains unclear how mil-lions of spiking neurons work in unison to realize the cogni-tive processes involved in memory search. In this paper, wepresent a biologically constrained neural network model thatperforms the task in a fashion similar to humans. The modelreproduces experimentally observed response timing effects,as well as similarity trends within and across semantic cate-gories derived from responses. Three different sources of theassociation data have been tested by embedding associationsin neural connections, with free association norms providingthe best match.