Unsteady-state (USS) core flood experiments provide data for deriving two-phase relative permeability and capillary pressure functions. The experimental data is uncertain due to measurement errors, and the accuracy of the derived flow functions is limited by both data and modeling errors. History matching provides a reasonable means of deriving in-phase flow functions from uncertain unsteady-state experimental data. This approach is preferred to other analytical procedures, which involve data smoothing and differentiation. Data smoothing leads to loss of information while data differentiation is a mathematically unstable procedure, which could be error magnifying. The problem is non-linear, inverse and ill posed. Hence the history-matching procedure gives a non-unique solution. This paper presents a procedure for quantifying the uncertainty ill two-phase flow functions, using unsteady-state experimental data. We validate the methodology using synthetic data. We investigate the impact of uncertain flow functions on a homogeneous reservoir model using the Buckley-Leverett theory. Using a synthetic, heterogeneous reservoir model, we estimate the uncertainty in oil recovery efficiency due to uncertainty in the flow functions.