A vehicular occupant restraining device, comprising: a side frame in a side section on an outer side, in the vehicle width direction, of a seat back of a vehicular seat; a side air bag arranged on an outer side, in a vehicle width direction, of the side frame, the side air bag receiving a gas supply from a first inflator to deploy by inflation, and the side air bag being interposed between an occupant seated in the vehicular seat and a vehicle interior side section; and an inside air bag arranged on an inner side, in the vehicle width direction, of the side frame in the side section, the inside air bag receiving a gas supply from a second inflator, the inside air bag deploying by inflation in the side section earlier and at a higher pressure than the side air bag, and the inside air bag pressing a seated occupant to an inner side in the vehicle width direction; wherein: the inside air bag is configured so as to deploy by inflation in a region more to a vehicle upper side than a second-from-bottom rib of six ribs provided in a torso of an AM50 type international standard side collision dummy, in a state in which the dummy is seated in the vehicular seat; the side frame has a side frame main body and, attached to the side frame main body, a reaction force-exerting section to which the inside air bag is attached and which exerts a reaction force on the inside air bag from an outer side in the vehicle width direction during deployment by inflation, and the reaction force-exerting section is inclined such that the more it heads toward a vehicle front side, the more it heads toward an outer side in the vehicle width direction, in a case in which the seat back is viewed in plane cross section. a side frame in a side section on an outer side, in the vehicle width direction, of a seat back of a vehicular seat; a side air bag arranged on an outer side, in a vehicle width direction, of the side frame, the side air bag receiving a gas supply from a first inflator to deploy by inflation, and the side air bag being interposed between an occupant seated in the vehicular seat and a vehicle interior side section; and an inside air bag arranged on an inner side, in the vehicle width direction, of the side frame in the side section, the inside air bag receiving a gas supply from a second inflator, the inside air bag deploying by inflation in the side section earlier and at a higher pressure than the side air bag, and the inside air bag pressing a seated occupant to an inner side in the vehicle width direction; wherein: the inside air bag is configured so as to deploy by inflation in a region more to a vehicle upper side than a second-from-bottom rib of six ribs provided in a torso of an AM50 type international standard side collision dummy, in a state in which the dummy is seated in the vehicular seat; the side frame has a side frame main body and, attached to the side frame main body, a reaction force-exerting section to which the inside air bag is attached and which exerts a reaction force on the inside air bag from an outer side in the vehicle width direction during deployment by inflation, and the reaction force-exerting section is inclined such that the more it heads toward a vehicle front side, the more it heads toward an outer side in the vehicle width direction, in a case in which the seat back is viewed in plane cross section. the inside air bag is configured so as to deploy by inflation in a region more to a vehicle upper side than a second-from-bottom rib of six ribs provided in a torso of an AM50 type international standard side collision dummy, in a state in which the dummy is seated in the vehicular seat; the side frame has a side frame main body and, attached to the side frame main body, a reaction force-exerting section to which the inside air bag is attached and which exerts a reaction force on the inside air bag from an outer side in the vehicle width direction during deployment by inflation, and the reaction force-exerting section is inclined such that the more it heads toward a vehicle front side, the more it heads toward an outer side in the vehicle width direction, in a case in which the seat back is viewed in plane cross section.