  The inverse problem of plane elasticity on $n$ equal-strength cavities in a
plane subjected to constant loading at infinity and in the cavities boundary is
analyzed. By reducing the governing boundary value problem to the
Riemann-Hilbert problem on a symmetric Riemann surface of genus $n-1$ a family
of conformal mappings from a parametric slit domain onto the $n$-connected
elastic domain is constructed. The conformal mappings are presented in terms of
hyperelliptic integrals and the zeros of the first derivative of the mappings
are analyzed. It is shown that for any $n\ge 1$ there always exists a set of
the loading parameters for which these zeros generate inadmissible poles of the
solution.
