jats:pA new, simple, formulation that describes capillary thinning as predicted by a two‐mode Giesekus model is derived, and its application in analyzing data from extensional rheometry (capillary thinning) experiments is discussed. An algorithm is presented that can be used to fit the expressions obtained from the Giesekus model to extensional rheometry data. Examples of data fitting are given for an idealized data set, for measurements obtained for aqueous solutions of 6 wt % 900,000 molecular weight polyethylene oxide, and for biological fluids obtained from pitchers of Nepenthes Rafflesiana. Good fits to the data were obtained, with coefficients of determination in excess of 0.98. For each data set, it was possible to calculate values of extensional viscosity and relaxation time for each of the two modes, allowing quantitative comparison of different fluids or of the same fluid as it ages. © 2016 American Institute of Chemical Engineers jats:italicAIChE J</jats:italic>, 62: 2188–2199, 2016</jats:p>