The attenuation model for Modified Mercalli intensities that is currently in use in New Zealand (Dowrick & Rhoades, 1999) was developed from the available intensity data from large local earthquakes in New Zealand, but it does not represent well the intensity patterns that are expected when large earthquakes occur on long faults (length 20 km or more). This is because very few such events have occurred in New Zealand in historical times. An attempt to account for elongated source geometries has resulted in a model which provides a plausible extension to the Dowrick & Rhoades model. It also addresses detail in the intensity data from New Zealand's four largest historical earthquakes, that has not previously been accounted for. In development of the new model, stochastic terms have been added to represent the effects of asperities or areas of large slip on the rupture surface and to account for uncertainty in the fitting of the original data.