The main result of this study is the development of attenuation expressions for Modified Mercalli intensity isoseismals in New Zealand earthquakes, in terms of magnitude Mw and source distance. Attenuation of isoseismal intensities has been modelled in a new 2-dimensional manner, i.e. in terms of three distance measures, i.e. radius a along the strike of the fault rupture, radius b normal to strike, and the mean radius c. Other factors which are included in the modelling are depth, focal mechanism, tectonic type (i.e. crustal, interface or dipping slab), and regional variations. As well as being implied in the source distance, the moderate effect of depth (to increase intensities) is modelled well with a separate linear depth term. Shallow (hc ≤ 60 km) Reverse mechanism events were found to give stronger intensities than Strike-Slip events which in tum were stronger than Normal mechanism events, the difference near source between Reverse and Normal events of Mw 7+ events being about 0.4 intensity units. Attenuation for the Central Volcanic Region and Deep events differs markedly from the Main Seismic Region. No magnitude saturation effects were found. Comparisons are made with some earlier New Zealand intensity models, and local and international peak ground acceleration attenuation models.