Earthquake Commission officials say they have received nearly 350 damage claims since the magnitude 7 quake off Taranaki on Tuesday.
EQC staff say most of the claims are of low value and for things such as contents damage and cracked plaster in people's homes.
The quake was centred offshore, 60km south of Opunake at a depth of 230km.
Most of the claims are from the lower West Coast of the North Island between New Plymouth and the Kapiti Coast.
EQC staff handling 50,000 damage claims from the December 2011 earthquake in Christchurch say they are confident of coping with the extra level of demand from this quake.
"There will be some issues we have to deal with around how widespread the claims are in terms of our ability to assess them," media manager Iain Butler says.
"But these are going to be very easily dealt-with claims."