Among types of trinucleotide repeats, there is some disproportion in the frequency of their occurrence in the human exome. This research presents new data describing the folding and thermodynamic stability of short, tandem RNA repeats of 23 types, focusing on the rare, yet poorly analyzed ones. UV-melting experiments included the presence of PEG or potassium and magnesium ions to determine their effect on the stability of RNA repeats structures. Rare repeats predominantly stayed single-stranded but had the potential for base pairing with other partially complementary repeat tracts. A coexistence of suitably complementary repeat types in a single RNA creates opportunities for interaction in the context of the secondary structure of RNA. We searched the human transcriptome for model RNAs in which different, particularly rare trinucleotide repeats coexist and selected the GABRA4 and CHIC1 RNAs to study intramolecular interactions between the repeat tracts that they contain. In vitro secondary structure probing results showed that the UAA and UUG repeat tracts, present in GABRA4 3′ UTR, form a double helix, which separates one of its structural domains. For the RNA CHIC1 ORF fragment containing four short AGG repeat tracts and the CGU tract, we proved the formation of quadruplexes that blocked reverse transcription.