Bidirectional sequential decoding (BSD) substantially reduces the computational variability of conventional sequential decoding without compromising the error performance. However, BSD does not completely eliminate the erasure problem. We propose an erasure-free decoding algorithm which combines the idea of BSD in conjunction with that of the multiple stack algorithm (MSA). It is found that the new bidirectional multiple stack algorithm (BMSA) offers substantial advantages over the MSA in terms of computational effort, memory requirements, and error performance. The BMSA appears as an attractive alternative to the Viterbi algorithm (VA) where low error probabilities and high decoding speeds are required.