"It would be difficult to think of a more problematic place on land to build a tunnel," NZTA Wellington state highways manager Rod James said.
Because of the very high water table, the ground directly under the existing road was sludgy and it would be "like building a tunnel through a swamp", he said.
Mr James said he recognised that the flyover would not please everyone.
"A big part of our job will be working with affected parties, urban designers, the Historic Places Trust and the councils to ensure that we design this project to respect the heritage and sensitivity of the surrounding environment."
Ms Wade-Brown said she was disappointed the NZTA found the tunnel option was not feasible.
She said the Wellington City Council would actively express its concerns about the environmental and urban design impacts of the flyover.
"Our principal aim is to ensure the flyover's impact on the Basin Reserve and the nearby Mt Victoria neighbourhood are minimised while ensuring the significance of the area is preserved. This historic precinct is too important to get wrong," she said.
She acknowledged that it was a significant investment to Wellington and she would like to see genuine commitment from the Government to invest in public transport at the same level as road building.
Mr James said the flyover decision was reached after extensive public consultation.
"Public feedback showed a clear preference for a pedestrian and cycleway to be attached to the bridge, so we've listened to this feedback and built it into our plans."
The plans for a flyover allowed for the already-approved plans to put Buckle Street underground to enable the new Memorial Park, funded by the government.
NZTA also looked into an alternative design proposed by Architecture Centre but said it was not considered workable because it would require significant property acquisition, a three and a half storey climb for pedestrians and cyclists numerous pedestrian and traffic problems and a large design footprint.
Wellington Central Labour MP Grant Robertson and Rongotai MP Annette King said the flyover decision was deeply flawed.
"The construction of a large concrete flyover beside the Basin Reserve is the wrong approach to dealing with transport issues in the area.
"There are alternatives that need to be revisited that will improve traffic flow without destroying the character of the area. Sadly, NZTA have failed to listen to the concerns of Wellingtonians and have ploughed on with a flawed proposal," they said in a joint statement.
NZTA had not properly considered the impact of the decision to create Memorial Park in Buckle street, they said.
The proposal was "half-baked".
"The plans released today do not even include a second tunnel through Mt Victoria, which while apparently still on the agenda is so far off it is not even worth putting in this plan."
"It's important to remember that the flyover proposal is subject to a separate decision making process from the Memorial Park. We urge NZTA to take a step back and look seriously at the alternative proposals for the Basin Reserve that will fit better with the Park, the amenity value of the Basin Reserve and the desire of Wellingtonians to have a long term, integrated sustainable solution to transport in the city."