Correctness of statement of the initial boundary-value problem for the three-dimensional equations in the hydrostatic approximation is considered at spectral expansion of the solution on the eigenfunctions of some vertical operator connected with equations. The horizontal expansion components are determined by solution of the two-dimensional shallow water equations for each dynamic mode. The equations in the curvilinear boundary-fitted coordinates are transformed into normal form suitable for numerical integration. The possibilities of generalization of such approach are discussed for the purpose of facilitation or removing its restrictions.