B737-700
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 216; Flight Crew Type 12600
Conflict Airborne Conflict; Flight Deck / Cabin / Aircraft Event Illness / Injury
Flight Crew Took Evasive Action; General Physical Injury / Incapacitation
Aircraft; Airspace Structure; Human Factors
ATC advised maintain FL200 for crossing traffic at FL190. Descending at 800-1;000 FPM got TCAS climb RA at FL208 and performed QRH procedure with climb of less than 1;000 feet. Advised ATC of RA climb and heard flight attendants discussing injuries in aft galley to 'B' and 'C' flight attendants. No other injuries. Six hours in hospital with no broken bones; but strained muscles and possible bruising. 'B' was most sore and was unable to sit on jump-seat for landing as she landed in the corner of galley on top of liqueur kit bottles. First Officer did an outstanding job calling out need for continued climb until clear of conflict. Never got a TA and red climb requirement to fly was tall. Uneventful landing and EMS met aircraft at the gate.Possibly sitting the flight attendants down earlier; but they were unfortunately cleaning up when a non-normal maneuver was performed for the safety of flight TCAS RA. We can't prepare them for that situation; as it is always a possibility.
B737 Captain reported a TCAS RA descending to FL200 with an aircraft at FL190. The response to the RA caused injuries to two Flight Attendants.