The paper studies an approach to numerical simulation of a semi-infinite ice floe effect on a floater dynamics. The authors have solved the problem numerically in a 2D formulation. The ice floe is considered as a semi-infinite beam with a bending stiffness equal to the cylindrical bending stiffness of a plate. Behavior of a floater under the actions of concentrated non-stationary and stationary harmonic forces is studied. Water is simulated as an ideal, incompressible fluid, and its flow is irrotational. The authors use nonlinear boundary conditions on the fluid free surface. The values of displacements and angles of rotation of the floater are found. It is found that at non-stationary regime maximum displacements and rotation angles of a floater can exceed their values at stationary regimes. The authors have revealed some cases when at nonlinear conditions on a fluid free surface floater’s displacements and angles of rotation exceed the displacements and angles of rotation of the floater at linear conditions. The calculations proved that it is not necessary to take into account the floater bending rigidity for parameters corresponding to real offshore structures.