The semantic fluency task has been used to understand the effects of semantic relationships on human memory search. A variety of computational models have been proposed that explain human behavioral data, yet it remains unclear how millions of spiking neurons work in unison to realize the cognitive processes involved in memory search. In this paper, we present a biologically constrained neural network model that performs the task in a fashion similar to humans. The model reproduces experimentally observed response timing effects, as well as similarity trends within and across semantic categories derived from responses. Three different sources of the association data have been tested by embedding associations in neural connections, with free association norms providing the best match.