  We investigate the exchange of mass in a binary system as a channel through
which a Be star can receive a rapid rotation. The mass-transfer phase in a
massive close binary system in the Hertzsprung-gap is accompanied by the
spinning up of the accreting component. We consider a case when the mass of the
accreting component increases by 1.5 times. The component acquires mass and
angular momentum while in a state of critical rotation. The angular momentum of
the component increases by 50 times. Meridional circulation effectively
transports angular momentum inside the component during the mass-transfer phase
and during the thermal time scale after the end of the mass-transfer phase. As
a result of mass transfer, the component acquires the rotation typical of
classical Be stars.
