**Flatmixed Problem for Elastic Rectangle**

The flat problem of elasticity theory for
rectangle, two sides of which are fastened and the other two sides are under the
influence of external tangent loadings is considered. For simplicity it is
assumed that external tangent loadings are absent.

The task is solved by means of Furie method.
The solution is presented in a form of the sum of the two Furie rows, each of
them contains four groups of free coefficient of integration. A part of free
coefficients is precisely determined, but for the determination of remain
coefficients of Furie rows the collection of four infinite systems of linear
algebraic equations is obtained. It is proved that infinite systems are quite
regular and their free members are tending to zero. Consequently, infinite
systems could be solved either through the method of progressive approximation
or the method of reduction.