With the availability of better estimates of magnitudes for large historical earthquakes, a 1978 study to model the Modified Mercalli intensities in large earthquakes in New Zealand has been revised. While instrumental measures of strong ground motion are obviously valuable, intensities will always be important because most of our large historical events predate the installation of accelerographs, and because intensity does seem to give a measure of the degree of damage. Crustal earthquakes in the Main Seismic Region have been divided into two classes on the basis of known or apparent focal depth. Events in the volcanic region are treated separately. No revision is attempted for shallow earthquakes in Fiordland or for events at greater than crustal depths anywhere in the country, the data base being too poor. Detailed goodness-of-fit statistics are presented: they compare favourably with those for the 1978 model and also for another model developed recently. The model is for the far field, so is useful for regional estimation of hazard but not for fault-specific studies at short distances. A companion paper addresses near-source modelling. Intensity is often assumed to be linearly related to the logarithm of ground motion parameters such as displacement or acceleration. This study shows that that assumption cannot hold over a range of distances. It may be possible to formulate a linear relationship at any particular distance, but the parameters of that relationship will change as distance is varied.