American Airlines flight AA1204, a Boeing 737-823, encountered severe turbulence during climb. ÿOf the 119 passengers and crew onboard, one flight attendant received a serious injury and another flight attendant received minor injuries.ÿ The airplane was not damaged. The captain was the pilot flying and the copilot was pilot monitoring. The flight was climbing through FL310 to the planned cruising altitude when the flight encountered moderate to severe clear air turbulence. According to the flight crew, the seatbelt sign was on when the turbulence occurred The turbulence subsided after about one and a half minutes and occurred during daylight, in visual meteorological conditions, and with no indications of convective weather in the area. At the time of the turbulence, two flight attendants (FA) had just started to prepare for beverage service in the aft galley when they were thrown to the floor. Both FAs crawled to the last row of seats as the turbulence continued. The two FAs were then assisted for the remainder of the flight by to passenger medical professionals. After landing, the FAs were transported to the hospital where one was diagnosed with a broken foot and the other with minor bruises. Probable Cause: An inadvertent encounter with clear air turbulence.