In this paper we present a novel, computationally and memory efficient way of modeling the spatial dependency of measured spike waveforms in extracellular recordings of neuronal activity. We use compartment models to simulate action potentials in neurons and then apply linear source approximation to calculate the resulting extracellular spike waveform on a three dimensional grid of measurement points surrounding the neurons. We then apply traditional compression techniques and polynomial fitting to obtain a compact mathematical description of the spatial dependency of the spike waveform. We show how the compressed models can be used to efficiently calculate the spike waveform from a neuron in a large set of measurement points simultaneously and how the same procedure can be inversed to calculate the spike waveforms from a large set of neurons at a single electrode position. The compressed models have been implemented into an object oriented simulation tool that allows the simulation of multielectrode recordings that capture the variations in spike waveforms that are expected to arise between the different recording channels. The computational simplicity of our approach allows the simulation of a multi-channel recording of signals from large populations of neurons while simulating the activity of every neuron with a high level of detail. We have validated our compressed models against the original data obtained from the compartment models and we have shown, by example, how the simulation approach presented here can be used to quantify the performance in spike sorting as a function of electrode position.