The mechanical properties of double-stranded RNA (dsRNA) are involved in many of its biological functions and are relevant for future nanotechnology applications. DsRNA must tightly bend to fit inside viral capsids or deform upon the interaction with proteins that regulate gene silencing or the immune response against viral attacks. However, the question of how the nucleotide sequence affects the global mechanical properties of dsRNA has so far remained largely unexplored. Here, we have employed state-of-the-art atomistic molecular dynamics simulations to unveil the mechanical response of different RNA duplexes to an external force. Our results reveal that, similarly to dsDNA, the mechanical properties of dsRNA are highly sequence-dependent. However, we find that the nucleotide sequence affects in a strikingly different manner the stretching and twisting response of RNA and DNA duplexes under force. We find that the elastic response of dsRNA is dominated by the local high flexibility of pyrimidine-purine steps. Moreover, the flexibility of pyrimidine-purine steps is independent of the sequence context, and the global flexibility of the duplex reasonably scales with the number of this kind of base-pair dinucleotides. We conclude that disparities of the mechanical response of dinucleotides are responsible for the differences observed in the mechanical properties of RNA and DNA duplexes.