This paper presents a beam search-based method for the stochastic assembly line balancing problem in U-lines. The proposed method minimizes total expected cost comprised of total labour cost and total expected incompletion cost. A beam search is an approximate branch and bound method that operates on a search tree. Even though beam search has been used in various problem domains, this is the first application to the assembly line balancing problem. The performance of the proposed method is measured on various test problems. The results of the computational experiments indicate that the average performance of the proposed method is better than the best-known heuristic in the literature for the traditional straight-line problem. Since the proposed method is the first heuristic for the stochastic U-type problem with the total expected cost criterion, we only report its results on the benchmark problems. Future research directions and the related bibliography are also provided in the paper.