Thousands of Massachusetts property owners are discovering their homes and businesses are in newly designated federal flood zones, forcing them to buy additional insurance coverage that can easily exceed $2,000 annually.

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The changes are the result of a Federal Emergency Management Agency project to remap flood zones, county by county nationwide. The agency plans to finish most of its Massachusetts maps by next summer, and local governments are in the process of notifying residents and business owners about the new zoning. At the same time, lenders are telling affected borrowers they must increase their insurance coverage.

Property owners across the state, confused and upset about the zoning changes, are calling local officials to complain and seek more information. FEMA designates a property as being in a flood area if historical data show it has a 1 percent or greater chance of flooding during any given year.

Michael Nakagawa, whose home is one of about 125 in Cambridge’s Alewife section recently included in a flood plain, is organizing neighbors to challenge the new zoning.

"We shouldn’t be forced to pay higher insurance rates and face lower property values because of the inaccuracies of their study," said Nakagawa, who lives near Alewife Brook. He hopes a surveyor can prove his home is safe from flooding because it is protected by an elevated sidewalk.

Catherine Daly Woodbury, storm water coordinator for the City of Cambridge, is sympathetic to the predicament of property owners, but just because a property hasn’t been under water before does not mean it can’t one day be flooded, she said.

"People are angry, and I try to point them in the right direction about where to get information for insurance and what their options are," Woodbury said. "Flood insurance is very expensive."

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In Cambridge, officials held community meetings and sent letters and fliers to Alewife property owners to inform them of their homes’ inclusion in the flood zone. Residents were advised to contact their insurance companies or to appeal the designation before the maps become effective there next June.

Woodbury, the storm water coordinator, said she has seen water surge from Alewife Brook, across Alewife Brook Parkway, and into the nearby neighborhood.

Phoebe Bernard, who has lived near Alewife Brook for 12 years, said she was not aware of the change until informed of it by the Globe.

Bernard said she received fliers, but did not read them. Her house has never flooded, she said, but several neighbors' basements have filled with water after storms.

"The last thing I need is to have my monthly expenses increase," said Bernard, 39, who is unemployed.

But she said she understands the reasoning behind improved mapping. "They set up flood zones for people's own protection," she said.