LAMINAR NEWTONIAN JETS HAVE BEEN STUDIED EXTENSIVELY AND A FULL ACCOUNT OF ALL SIGNIFICANT THEORETICAL AND EXPERIMENTAL WORK IS GIVEN BY SCHLICHTING (1968).THE BOUNDARY LAYER THEORY AND THE SIMILARITY SOLUTIONS GIVEN BY SCHLICHTING HAVE ALSO BEEN EXTENDED TO LAMINAR NON-NEWTONIAN JETS.LEMIEUX AND UNNY (1968) AND ATKINSON (1972) DEVELOPED SIMILARITY SOLUTIONS FOR THE TWO-DIMENSIONAL JET AND ROTEM (1964) FOR THE AXISYMMETRIC JET OF A POWER-LAW FLUID ISSUING INTO A MASS OF THE SAME FLUID.LAMINAR NON-NEWTONIAN JETS ARE PERHAPS MORE REALISTIC THAN NEWTONIAN.MANY NON-NEWTONIAN FLUIDS, SUCH AS POLYMER SOLUTIONS AND MELTS, HAVE LARGE APPARENT VISCOSITIES AND LAMINAR FLOW PERSITS UNDER USUAL PROCESSING CONDITIONS.A STUDY OF JETS OF SUCH FLUIDS IS OF BASIC INTEREST IN POLYMER MIXING, EXTRUSION,.INJECTION MOULDING, AND DRAG REDUCTION.ACTUALLY POLYMER SOLUTIONS AND MELTS EXHIBIT ELASTIC EFFECTS IN ADDITION TO NON-NEWTONIAN BEHAVIOUR.ACCORDINGLY A COMPLETE STUDY SHOULD INCLUDE NORMAL STRESS DIFFERENCES.IN THE PRESENT PAPER AN ATTEMPT IN THAT DIRECTION IS MADE BY EXAMINING FIRST THE SIMPLER INELASTIC PROBLEM.THE PRESENT NUMERICAL METHOD WAS DEVELOPED BECAUSE THE EXISTING SIMILARITY SOLUTIONS ARE VALID ONLY IN LARGE DISTANCES FROM THE JET ORIFICE ALTHOUGH IN THE CHEMICAL ENGINEERING APPLICATIONS MENTIONED ABOVE THE EARLY PART OF THE FLOW IS MORE IMPORTANT.