The conjugate-factorized model of the problem of sagging of thin plate is formulated in the work. The statements in “saggings” and “moments” are described. It is shown that in both cases the problem operator has the conjugate-factorized structure $P^*BP$, where $P$ is a differential matrix-operator of the second order, and $B$ is a numerical matrix. The presented results are analogous to those obtained for the problems of elasticity theory and give the posibility to use the method of support operator to build the difference scheme, and to apply the iteration methods in subspace or the direct method of step by step conversion for the numerical solution to the difference problem.