Background: RNA deleterious point mutation prediction was previously addressed with programs such as RNAmute and MultiRNAmute. The purpose of these programs is to predict a global conformational rearrangement of the secondary structure of a functional RNA molecule, thereby disrupting its function. RNAmute was designed to deal with only single point mutations in a brute force manner, while in MultiRNAmute an efficient approach to deal with multiple point mutations was developed. The approach used in MultiRNAmute is based on the stabilization of the suboptimal RNA folding prediction solutions and/or destabilization of the optimal folding prediction solution of the wild type RNA molecule. The MultiRNAmute algorithm is significantly more efficient than the brute force approach in RNAmute, but in the case of long sequences and large m-point mutation sets the MultiRNAmute becomes exponential in examining all possible stabilizing and destabilizing mutations. Results: An inherent limitation in the RNAmute and MultiRNAmute programs is their ability to predict only substitution mutations, as these programs were not designed to work with deletion or insertion mutations. To address this limitation we herein develop a very fast algorithm, based on suboptimal folding solutions, to predict a predefined number of multiple point deleterious mutations as specified by the user. Depending on the user’s choice, each such set of mutations may contain combinations of deletions, insertions and substitution mutations. Additionally, we prove the hardness of predicting the most deleterious set of point mutations in structural RNAs. Conclusions: We developed a method that extends our previous MultiRNAmute method to predict insertion and deletion mutations in addition to substitutions. The additional advantage of the new method is its efficiency to find a predefined number of deleterious mutations. Our new method may be exploited by biologists and virologists prior to site-directed mutagenesis experiments, which involve indel mutations along with substitutions. For example, our method may help to investigate the change of function in an RNA virus via mutations that disrupt important motifs in its secondary structure.