Mayor Kirsten Wise last night declared a state of emergency.
Weather experts have called yesterday's event "record breaking" and it is now officially the second wettest day in the city since records began.
National Institute of Water and Atmospheric Research said yesterday's downpour was 423 per cent of what was normally seen in the whole month of November - in a single day.
As of about 10pm yesterday, 237mm of rain had been recorded since 9am.
Thousands of people in the area have been without power since late last night.
Officials said more than 3300 people had been left in the dark after yesterday's major storm flooded Napier.
A statement from lines company Unison said up to 3370 customers around Napier were without electricity about 10.15pm yesterday.
Unison spokesman Danny Gough said conditions were too rough for crews to continue work through the night.
"Heavy rain and widespread flooding throughout the day, combined with darkness setting in, has made the conditions too unsafe for our crews to continue to operate.
"The safety of the public and our crews is paramount and hence we have made the decision to stand our crews down until first light."
He thanked the public for their patience and said all their available resources were on standby to start repairs this morning - weather permitting and on condition of floodwaters subsiding.
"Our crews will still attend to any emergency situations if required," he said.
"We are also mindful of our customers who are medically dependent on power, so we urge them to make alternative arrangements and liaise with their medical providers for advice."
Parents are being told by local schools to keep children home today, as staff work to assess their respective school grounds as well.
A number of schools have already issued notices via Facebook. Those closed include Porritt School, Tamatea Primary, Tamatea Intermediate, Fairhaven School and Tamatea High.
The Hawke's Bay Civil Defence is working with emergency services again this morning.
A freephone number has been set up for anyone needing welfare support - including food and clothing.
Those who have been displaced by the flooding are also urged to make contact via 0800 422 923.
During power outages, Unison regularly advises the following safety precautions:
• Check for fallen or damaged electricity lines. Never touch wires or lines lying on the ground, hanging from poles, or objects such as tree branches that may be touching them. Fallen lines or wires may still be carrying an electrical current and could shock, injure or even kill if touched. Unison is urging anyone who sees a power line down to call 0800 2 UNISON.
• Turn off the power at the main switch if you suspect any electrical damage in your home. If the power goes out, turn off all electrical appliances to prevent possible damage by a power surge when the electricity supply is restored.
• Remember that if the electricity network is damaged, it might take some time to get reconnected, so make sure you have a battery-operated radio, a torch, spare batteries, and a full gas bottle for your BBQ as part of your emergency kit.
• Medically dependent customers are advised to prepare for the likelihood of no power and make alternative arrangements in advance.