Plane and axisymmetric, laminar, submerged jet flows of non-Newtonian power-law fluids, issuing from an orifice in a wall, are investigated for large Reynolds numbers. In contrast to previous investigations,the interaction between the jet flow and the induced flow is taken into account using matched asymptotic expansions combined with a two-scaling technique. The following four effects, occuring at sufficiently low values of the power-law index, are analyzed:• Very large mass entrainment into the jet.• Non-negligible viscosity in the induced outer flow.• Slow, but substantial, variation of the momentum flow in the jet with increasing distance from the orifice. • Spreading of the jet into a recirculatory flow (eddy). The analytical results are compared with experimental data taken from the literature. For the purpose of further comparisons, and in order to extend the investigation into flow regimes where the asymptotic expansion ceases to be valid, the full equations of motion are solved numerically by means of a finite element code. Mathematics Subject Classification (2000). 35Q30, 35Q35, 41A60, 65Z05, 76D05, 76D09, 76D10, 76D25.