We consider Mityuk’s function and radius which have been proposed in [15]as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk’s function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is based on the boundary integral equation with the generalized Neumann kernel. Special attention is given to the validation of the theoretical results on the existence of critical points and the boundary behavior of Mityuk’s radius.