After years of suing thousands of people for allegedly stealing music via the Internet, the recording industry is set to drop its legal assault as it searches for more effective ways to combat online music piracy.

The decision represents an abrupt shift of strategy for the industry, which has opened legal proceedings against about 35,000 people since 2003. Critics say the legal offensive ultimately did little to stem the tide of illegally downloaded music. And it created a public-relations disaster for the industry, whose...