The steady and transient behavior of jets generated by circular and slit nozzles are analyzed by the Galerkin finite‐element method with free‐surface parametrization and Newton iteration. A novel constitutive equation is used to approximate Bingham liquids that is valid uniformly in yielded and unyielded domains and which approximates the ideal Bingham model and the Newtonian liquid in its two limiting behaviors. At steady state the influence of yield stress on the die swell is equivalent to that of surface tension; that is, suppression of jet diameter at low Reynolds numbers and necking at high Reynolds number. The predictions at high Reynolds numbers agree with the asymptotic behavior at infinite Reynolds number of the jet far downstream. In the transient analysis, surface tension destabilizes round jets and increases the size of satellite drops.Yield stress was found to retard jet breakup times in addition to producing smaller satellites. Shear thinning was found to result in shorter collapse times than those for Newtonian fluid; furthermore, the satellite drop size increased with increasing shear thinning. The nonlinear analysis predicts that, although round jet breakup may occur spontaneously by surface tension, an external factor, commonly air shear, must be applied to break a planar jet at Reynolds numbers below its transition to a turbulent jet.