In this work, the boundary layers over a continuously shrinking sheet with a power-law surface velocity and mass transfer were investigated. Based on the boundary layer assumptions, the similarity equations with a controlling parameter 13 were obtained and solved numerically. Theoretical analysis was conducted for certain special conditions and exact solutions were derived for beta = -1 and beta = -2 and also for the power index m = -1. Numerical techniques were used to solve the similarity equation for other parameters. Quite different and interesting solution behaviors were found for a shrinking sheet compared with a stretching sheet. Multiple solutions were obtained for certain mass transfer parameter and controlling parameter beta. Velocity overshoot near the wall and near the boundary layer edge were observed for certain solution branches. The current results for a power-law shrinking sheet offer quite interesting nonlinear behaviors and greatly enrich the solution and understanding of boundary layers. (c) 2008 Elsevier Ltd. All rights reserved.