Recently, the use of mathematical methods and computer science applications have got significant response among biochemists and biologists to modeling the biological systems. The computational and mathematical methods have enormous potential for modeling the deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) structures. The modeling of DNA and RNA secondary structures using automata theory had a significant impact in the fields of computer science. It is a natural goal to model the RNA secondary biomolecular structures using quantum computational models. Two-way quantum finite automata with classical states are more dominant than two-way probabilistic finite automata in language recognition. The main objective of this paper is on using two-way quantum finite automata with classical states to simulate, model and analyze the ribonucleic acid (RNA) sequences.