Summary: A boundary integral method is presented for constructing approximations to the mapping functions of bounded multiply connected regions to the standard canonical slit domains given by Z. Nehari
[“Conformal Mapping", (International Series in Pure and Applied Mathematics) New York-Toronto- London: McGraw-Hill Book Company, Inc. VIII, 396 p. (1952; Zbl 0048.31503
)]. The method is based on expressing the mapping function in terms of the solution of a Riemann-Hilbert problem which can be solved by a uniquely solvable boundary integral equation with the generalized Neumann kernel. Three numerical examples are presented to show the effectiveness of the present method.