Abstract An incremental fold test method for the paleostress inversion of a fault-slip dataset obtained from folded sedimentary rock is proposed. The method provides not only the orientations of the three principal stress axes and the stress ratio, but also the relative timing of folding and faulting. The method is based on the stepwise backtilting of strata. Significant stresses are identified by simply comparing peak values of total goodness of fit for the paleostress inversion technique and the stress differences among peaks detected from each step of backtilting of a fault-slip dataset. To assess its validity, the method is applied to artificial fault-slip datasets generated with hypothetical histories of folding, and faulting and with known paleostresses. The proposed method successfully recovers the artificial stress tensors and the relative ages of folding and faulting. Second, the method is applied to a natural fault-slip dataset obtained for Eocene sedimentary strata in Kyushu, southwest Japan, folded around NE–SW-trending axes in the Miocene. The analysis yields three significant paleostresses: a normal-faulting stress that occurred before folding, and two syn-folding stresses, indicating the existence of a spatially and temporally varying stress field during folding.