This review describes methods and techniques developed to date for measuring elongational stresses produced in elongational flows. Experimental results are presented and it is shown that in many cases the strain exerted on a fluid element is important for the stress in elongational flow fields of dilute and nondilute polymer solutions. In several cases, however, it is demonstrated that the elongational stress is correlated with the elongational rate and agrees with the prediction of the FENE dumbbells model of the second-order type.