A medical stopcock is provided that is constructed and arranged to withstand high pressures and gamma irradiation. The stopcock generally includes a housing and a valve member. The valve member is trapped within the housing so that, when subjected to relatively high pressures, the valve member is unlikely to become separated from the housing. A handle member is attached to the valve member and allows the valve member to be rotated from open to closed positions. In some preferred embodiments, the handle member locks the valve member within the housing, when attached. All of the components are constructed of gamma-stable materials so that the stopcock may be sterilized, in its package, using gamma irradiation.