A convenient way of measuring normal thrusts on fluid‐immersed surfaces is by use of a pressure gauge attached to a hole in the surface. With viscoelastic fluids exhibiting normal stress effects, it is shown that a systematic error exists, independent of hole size, but dependent on wall shear stress. Experiments were made in an open channel with various holes from 132 in. to 14 in. diameter, and also with an 18 in. wide slot. Errors were small with 30P silicone fluid, but with two viscoelastic solutions errors were always negative and of the order of 25% of the first normal stress difference. No significant difference has been seen yet between sharp‐edged holes of different sizes or between holes and slots. A theoretical treatment for plane creeping flow over a deep slot predicts that the error is negative, independent of slot width, and 25% of the first normal stress difference. Some implications for normal stress measurements are considered.