Abstract <p>Modifications of a standard quadrature formula for a single-layer potential for the Helmholtz equation in the case of a triangulated surface are considered. In contrast to the standard quadrature formula, the modified ones provide a uniform approximation of the single-layer potential and preserve its continuity across the surface where the potential density is specified. The properties of the modified quadrature formulas are confirmed by numerical tests that compare the numerical accuracy of different formulas for different parameter values. Based on the numerical tests, the optimal choice of parameters in the modified formulas is discussed.</p>