Middle class Americans are getting squeezed out of the east and west coasts by expensive home prices. So they're heading to the middle of the country, The New York Times reports.

The country's five fast growing cities between 2006 and 2012 were Austin, Texas (22 percent); Raleigh-Durham, N.C. (18 percent); San Antonio, Texas (16 percent); Charlotte, N.C. (16 percent); and Provo, Utah (16 percent), according to Redfin, a national real estate brokerage firm.

"This is the opposite of the gold rush," Tony Trammell, who moved with about a dozen friends from San Diego to a $260,000, 3,300-square-foot house outside Oklahoma City, tells The Times.

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As for the role of home prices, the portion of those moving more than 500 miles who said housing represented the main reason for their flight has climbed to 18 percent this year from 8 percent in 2007, according to the Census Bureau.

"A large percentage of Americans had to read 'The Grapes of Wrath,'" Oklahoma City Mayor Mick Cornett, tells The Times. He was referring to the John Steinbeck novel about Oklahomans fleeing to California during the Depression.

Now those migrants' descendants are traveling the reverse route. "It's 'The Wrath of Grapes,'" he quips.

Nationally, home price increases are slowing. The S&P/Case-Shiller index of home prices in 20 metropolitan areas slipped a seasonally-adjusted 0.3 percent in May from April. And the index rose 9.3 percent in the 12 months through May, the slowest pace since February 2013.

"The way these markets go, that [0.3 percent dip] could be a turning point," Nobel laureate economist Robert Shiller of Yale University tells CNBC. "There's some clear evidence of a weakening."

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