It claims Samsung's Galaxy range of mobile phones and tablet "slavishly" copy the iPhone and iPad, according to court papers.
Apple's claims focus on Galaxy's design features, such as the look of its screen icons.
Galaxy products use Google's Android operating system, which directly competes with Apple's mobile software.
As well as being a competitor, Samsung supplies Apple with microchips that are used in some Apple products, such as the A4 and A5 processors, as well as memory chips used in MacBook Pro computers.
The lawsuit was filed on Friday and alleges Samsung violated Apple's patents and trademarks.
Apple spokeswoman Kristin Huguet said in a statement: "This kind of blatant copying is wrong."
Samsung was not immediately available for comment.
John Jackson, an analyst with CCS Insight, said Samsung is essentially Apple's only real tablet competitor at this stage.
Apple is one participant in a web of litigation among phone makers and software firms over who owns the patents used in smartphones.
Nokia has sued Apple, which in turn has sued handset maker HTC Corp.
Apple is bringing 16 claims against Samsung, including unjust enrichment, trademark infringement and 10 patent claims.
In March Apple sued HTC alleging patent infringement over the iPhone.
In October 2010, Apple sued Motorola, saying its smartphones use Apple's intellectual property.
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