The development of efficient methods for predicting secondary structures of single stranded nucleic acids is of great importance in understanding many fundamental processes in genetics and molecular biology. The presently available energy minimization techniques yield only one structure which is often different from biologically significant RNA secondary structures. Application of these computationally complex algorithms is limited to relatively short RNA strands. We propose that folding patterns of RNAs be predicted by employing an algorithm based on Monte Carlo methods of statistical mechanics, which includes an annealing procedure. Monte Carlo methods, in contrast to minimization routines, scan many local minima, calculate statistically averaged properties, and predict melting patterns. These methods are not limited by computer storage requirements and, therefore, can handle RNAs of the order of a few thousand nucleotides. Preliminary results for small RNAs are presented and a feasibility study is proposed to evaluate the efficiency of the new algorithm, determine melting and refolding of short RNA molecules, and predict secondary structures of selected long RNAs is proposed. Long term goals include generalization and further improvement of the algorithm and the development of a rapid and reliable software for analysis of large RNA segments. Both the method and the results of the proposed studies are expected to be of interest to the scientific and business communities in the health related areas of pharmacology, genetic engineering, and molecular biology.