  A solution of the elliptic type PDE of the 4th order, being a reduction of
the Eqs. of stress function corresponding to any case of plane anisotropy which
is not equal to isotropy (proved by S.\,G.~Mikhlin), is described in terms of
hypercomplex `analytic' functions with values in two-dimensional semisimple
algebra over the field of complex numbers in case when a domain under
consideration is bounded and simply-connected. A boundary value problem on
finding a function which satisfies this PDE in the considered domain (bounded
and simply-connected) and permits continuations (to the boundary) of operators
$\frac{\partial}{\partial x}$ and $\frac{\partial}{\partial y}$ acted to it, is
reduced to certain BVP for these hypercomplex functions.
