Abstract The elastic hole pressure for plane, steady, creeping shear flow over a transverse slot of a Johnson-Segalman fluid is studied numerically. To correctly apply the theory of Higashitani, Pritchard, Baird and Lodge (HPBL), we start with a modified hole-pressure relation (MHPR) and simulate the hole-pressure measurement using the finite element method and the multiple-mesh extrapolation technique. The path integrals in MHPR and HP are evaluated to check the error cancellation phenomenon and a full instrument simulation is conducted to predict N 1. The agreement between numerical simulation and analytical prediction is satisfactory, within the range of De⩽ 1. This study suggests that N 1 can be predicted via the hole-pressure measurement to a sufficient approximation for the Johnson-Segalman model.