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This paper contains calculations of (a) the effect of a circular hole on sheet‐resistance readings as measured by a four‐point probe; (b) a solution to the generalized four‐point probe measurement on a thin circular disk, regardless of the shape, position, and orientation of the probe. The first analysis is intended to aid in the estimation of the effect of pinholes in thin films, and also in certain thin‐film circuits where holes have been deliberately made in the substrates. The greatest effect on a linear and evenly spaced four‐point probe is found when a hole is just touching one of the potential probes. It is shown that an effect of up to +100% or -40% can result from a hole whose diameter equals the probe spacing, depending upon its position relative to the probes. Analytical expressions are developed for several limiting cases, including that of a straight‐edge boundary, in which case the results coincide with earlier work. The second analysis can be used to calculate the sheet resistance of a thin semiconductor wafer, and to evaluate its uniformity. For certain special cases, the present analysis coincides with results obtained elsewhere.