It has lost more than 90% of its value over the past years, as it struggled to attract customers to its often outdated stores.
In the Delaware court filing, RadioShack said it had $1.2bn in assets and $1.38bn in debt.
RadioShack, which first opened in 1921 as a mail-order retailer, currently operates 4,485 stores across the US.
The company sells everything from mobile phone accessories to converters and power cables.
In its bankruptcy filing, the firm said it planned to sell up to 2,400 stores to shareholder Standard General.
RadioShack was de-listed from the New York Stock Exchange (NYSE) earlier in the week.