  A nonlinear inverse problem of antiplane elasticity for a multiply connected
domain is examined. It is required to determine the profile of $n$ uniformly
stressed inclusions when the surrounding infinite body is subjected to
antiplane uniform shear at infinity. A method of conformal mappings of circular
multiply connected domains is employed. The conformal map is recovered by
solving consequently two Riemann-Hilbert problems for piecewise analytic
symmetric automorphic functions. For domains associated with the first class
Schottky groups a series-form representation of a ($3n-4$) parametric family of
conformal maps solving the problem is discovered. Numerical results for two and
three uniformly stressed inclusions are reported and discussed.
