Аннотация:The specific features of the application of modified Newton's method
to approximate analytical solution of a class of nonlinear elasticity prob-
lems under finite plane strains are described. This class of problems
includes problems of stress distribution around holes in infinite nonlin-
ear elastic bodies. The problems are solved within the framework of
the theory of superimposed finite strains. It is assumed that holes are
originated in previously loaded bodies undergoing finite homogeneous
initial strains. The specific features mentioned above are related with
the necessity to obtain functions in right parts of linearized equations in
a form that admits analytical integration. For this purpose, the equa-
tions and boundary conditions are written in a special form using the
Cayley{Hamilton theorem and some changes of variables. The analysis
is performed for the materials of Mooney type. Some numerical results
are given.