One of the most interesting aspects of penicillin-induced epileptiform activity in the hippocampal slice preparation is that CA3 pyramidal cells periodically burst in synchrony. Penicillin is now known to block inhibitory postsynaptic potentials and permit excitatory postsynaptic potentials to trigger bursting in single neurons. The phenomenon of synchronous bursting is readily simulated with a simple but realistic quantitative model, assuming that CA3 pyramidal cells are mutually excitatory. The degree of coherence in the population burst depends on the connectivity of the cells with each other and on the amount of coupling between them. If coherence is extremely high, then a given cell must be able to excite a number of other cells in its neighborhood, and conversely, any one cell can be triggered to burst by bursting in only one of its neighbors. Such predictions are in principle experimentally testable. This model does not predict the experimentally observed relation between the periods of spontaneous single cell bursting and synchronous bursting of the population (single cells burst more rapidly in the resting slice than does the population in the penicillin-treated slice). We offer plausible testable explanations for this discrepancy. © 1981.