A new computational approach to study correlated neural activity is presented. Simulating Elementary Neural NEtworks for Correlation Analysis (SENNECA) is a specific-purpose simulator oriented to small circuits of realistic neurons. The model neuron that it implements can reproduce a wide scope of integrate-and-fire models by simply adjusting the parameter set. Three different distributions of SENNECA are available: an easy-to-use web-based version, a Matlab (Windows and Linux) script, and a C++ class library for low-level coding. The main features of the simulator are explained, and several examples of neural activity analysis are given to illustrate the potential of this new tool.