Three methods of approximating the power of Wilcoxon's rank-sum test against shift alternatives are studied. They are obtained by using a Gaussian assumption, Edgeworth expansion, or bootstrap. It is assumed that a historical data set is available to use in estimating the shape of the distribution. The methods are compared through simulation across several different distributional types. The results indicate that the bootstrap generally gives the most reliable approximation, however the Edgeworth expansion has the practical advantage that a lower bound on the power can be roughly approximated. The methods are illustrated on muscle strength data from patients with osteogenesis imperfecta. Published in 1999 by John Wiley & Sons, Ltd. This is US Government work and is in the public domain in the United States.