The hydrodynamic and thermal boundary layer similarity flows driven past a semi-infinite impermeable flat plate by a power-law shear with asymptotic velocity profile Uinfinity(y) = betay(-1/2) (y --> infinity, beta > 0) is considered (y denotes the coordinate normal to the plate). Assuming that the buoyancy and viscous dissipation effects may be neglected, the special cases of an isothermal and of an adiabatic flat plate are examined both analytically and numerically. (C) 2003 Elsevier Ltd. All rights reserved.