In this paper, problems of ice sheet and hydroelastic waves interaction simulation are studied. Linear equation of thin elastic plate is used as a basic model. Topicality of the problem is described in introduction. Linear equation of thin plate is studied in section 1. Basic assumptions of the elastic plate model for ice sheet modeling are considered. Problems of infinite ice sheet deflection under a moving load are investigated in section 2. Problem formulation for the load motion along a continuous ice cover is provided along with the examples of cracks and shock pulses modeling. Methods and results of numerical studies are considered. The proposed method of calculation can be used for rectilinear and curvilinear motions of the load. Problems of the ice sheet and buildings interaction are investigated for cases of the ice sheet interaction with one wall and the ice sheet clamped to the channel walls (section 3). A specific feature of the problem of ice sheet behavior in a channel is that only hydrodynamic pressure is considered with no external load. Results of numerical calculations are discussed. Influence of snow and temperature stresses on ice sheet parameters is investigated in section 4. A small oscillation equation for a floating viscoelastic ice plate covered with snow is presented. Comparison of numerical calculations with experimental data is discussed.