Mobile phone makers shipped 361 million handsets in the second quarter of this year, up 13% on the same period in 2010, according to a new report.

Smartphone volumes reached 110 million units, with Apple overtaking Nokia and Samsung to become the biggest vendor, said the Strategy Analytics report. Nokia was the biggest maker of all types of handsets, but volumes fell 20% to 88.5 million units for the quarter. Nokia’s market share dipped to 25% – its lowest level since 1999.

Samsung, the number two handset maker, shipped 74 million units, rising 16% from 63.8 million in the quarter a year earlier. The company’s market share rose to just above 20%, and Samsung is now “breathing down Nokia’s neck”, the report said. Strategy Analytics said Nokia was plagued by problems.

“An unexciting touchphone portfolio, inventory corrections in Asia and Western Europe, wavering demand for the Symbian platform and limited presence in the huge US market continue to weigh on Nokia’s near-term performance,” the report said. The report describes Apple as the “star performer” during the quarter, more than doubling its handset shipments to a record 20.3 million units. Apple’s market share was 6%, just over 1 point behind LG, the number three manufacturer.

LG shipped 24.8 million handsets during the three months, with volumes down 19% from a year earlier. China-based ZTE shipped 18 million handsets, giving it a global market share of 5%.