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The results of numerical simulation of the neutron generation process in the cone lead targets exposed to laser irradiation are presented. The experimental time dependence of the target shell is used as a boundary condition for the hydrodynamic equations. Deuterium compression is calculated on the assumption that some part of the shell that continues to move inward onto the conical target is decelerated by deuterium in the absence of the reactive force. The behavior of deuterium is described by the 2D equations of two temperature gas dynamics with the electron and ion contributions to the heat conduction taken into account. The behavior of lead is described by the 2D equations of gas dynamics closed by the real wide range equation of state (EOS). The neutron yield in the experiments under discussion is caused by short duration steep rises of the ion temperature generated by the collapse of the heading shock wave and the first reflected one. The stage of adiabatic compression of the high-temperature plasma was lacking in the experiment due to the small mass of the shell.