The finite element seismic (linear spectral and dynamic) analyses of stability and stress-strain state of a new type of composed Faced Symmetrical Hardfill (FSH) dam with central zone of rockfill enriched with cement mortar (REC) or FSH-REC dam of different heights (30, 60 and 100 m) and slopes (0.4, 0.5 and 0.7 H/1V) on rigid and soft foundations are performed and compared with the traditional gravity RCC dams. The methodology of seismic response of the system "dam-foundation-reservoir" is considered in brief as well as the elastoplastic hardening model of RCC taking into account the cohesion and angle of inner friction of RCC joints. The seismic resistance of the 100 m high FSH-REC dam (with slopes of 0.5 H/1H) on rock foundation is considered for action of two strong earthquakes (MDE and MCE) with ground horizontal and vertical accelerograms with peak values of 0.2 and 0.4 g. In the MDE case the dam behavior is quite elastic and safe with no tension or opening of RCC joints. In the MCE case the dam behavior is elastoplastic with plastic deformations near the dam crest and partial opening of RCC joints in the lower half of the dam. The upstream CARPI membrane can provide the water-tightness of the dam in the MDE and MCE cases.