Alphaviruses are mosquito-borne pathogens that cause human diseases ranging from debilitating arthritis to lethal encephalitis. Studies with Sindbis virus (SINV), which causes fever, rash, and arthralgia in humans, and Venezuelan equine encephalitis virus (VEEV), which causes encephalitis, have identified RNA structural elements that play key roles in replication and pathogenesis. However, a complete genomic structural profile has not been established for these viruses. We used the structural probing technique SHAPE-MaP to identify structured elements within the SINV and VEEV genomes. Our SHAPE-directed structural models recapitulate known RNA structures, while also identifying novel structural elements, including a new functional element in the nsP1 region of SINV whose disruption causes a defect in infectivity. Although RNA structural elements are important for multiple aspects of alphavirus biology, we found the majority of RNA structures were not conserved between SINV and VEEV. Our data suggest that alphavirus RNA genomes are highly divergent structurally despite similar genomic architecture and sequence conservation; still, RNA structural elements are critical to the viral life cycle. These findings reframe traditional assumptions about RNA structure and evolution: rather than structures being conserved, alphaviruses frequently evolve new structures that may shape interactions with host immune systems or co-evolve with viral proteins.