More than 200 stores will close within days.
Bankruptcy is often a tool that retailers use to get out of unwanted leases.
As a result of the store closures and other operational changes, Mattress Firm's corporate earnings before interest, tax, depreciation and amortization (EBITDA) are expected to be $200 million by the company's 2020 financial year, Steinhoff said. Mattress Firm locations in Ballwin and Richmond Heights also will close.More news: At least 11 dead after 5.9 magnitude quake in Haiti
Photo of Mattress Firm in downtown Silver Spring by Mike Diegel.
FILE -Mattresses are offered for sale at a Mattress Firm store on December 6, 2017 in Chicago, Illinois. The stock is down more than 18 percent this year.
The company's filing comes only days after Amazon said it would delve into the online "bed-in-a-box" business.
"Traditional mattress retailers have been alienating customers for decades and are now buckling under pressure", Philip Krim, the CEO and co-founder of Casper, said in a statement. Steinhoff's offer of $64 a share was more than double the company's stock price of $29.74 at the time. Its shares are down almost 54 percent since January.More news: Trio win Nobel Chemistry Prize for 'a revolution in evolution'
"The Mattress Firm recapitalization also represents a further positive step in the wider Steinhoff restructuring process", van de Merwe said.
The retailer has secured about $250 million in so-called "debtor-in-possession" financing to support its operations under bankruptcy.
The company, which has almost 10,000 employees, said it filed motions to support the continued payment of employee wages and health and welfare benefits.
The company is asking a bankruptcy court in DE for permission to terminate up to 700 leases.More news: South Korea jails ex-president Lee Myung-bak