Reaction mechanisms of hydrosilylation of ketone and alkene with tertiary silane using the Wilkinson-type catalyst were theoretically investigated on the basis of density functional calculations using ωB97XD functional. Previously proposed three mechanisms, the Chalk-Harrod (CH) mechanism, the modified Chalk-Harrod (mCH) mechanism, and the outer-sphere mechanism were examined. Besides, we also found two mechanisms, the alternative CH (aCH) mechanism and the double hydride (DH) mechanism. In the aCH mechanism, a four-coordinate rhodium hydride complex formed through the elimination of R3Si-Cl is a catalytically active species. In the DH mechanism, the active species is a six-coordinate complex with two Rh-H bonds. For the C═O double bond hydrosilylation, the rate-determining steps of the aCH and DH mechanisms are both acetone insertion into the Rh-H bond, and the order of the activation barrier is DH < aCH ≈ CH < mCH. For the C═C double bond hydrosilylation, except for the mCH pathway whose rate-determining step is the hydrosilane addition reaction, the rate-determining steps of the CH, aCH, and DH pathways are Si-C reductive elimination reactions. The order of the energy barrier is DH ≈ mCH < aCH ≈ CH. In the outer-sphere mechanism, no stable intermediate or transition state was found. Consequently, we concluded that the DH mechanism is adopted as the mechanism for the Rh-catalyzed hydrosilylation of the carbonyl group while the mCH or DH mechanism is adopted as the mechanism for alkenes under conditions where their active intermediates are formed. The present result revises a hypothesis that the hydrosilylation of the carbonyl group is in general accomplished by the mCH mechanism. The active species in the DH mechanism has one more extra Rh-H bond compared to that of the other pathways, and its interaction with a silyl group, trans-influence, and small steric effect are the origin of the highly efficient catalytic activity, which was not reported before.