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This paper considers the ultimate (under heating conditions) kinematic characteristics of composite solid bodies accelerated by a unsteady-state magnetic-field pressure. The accelerated sheet comprises two layers: a layer of a composite material consisting of a mixture of two materials with different electrothermal properties, and a homogeneous material layer. Variation of the electrical properties of the composite layer with the coordinate is achieved by changing the volume concentration of its constituent materials. For an exponential magnetic field rise, an analytical solution is obtained for the problem of finding the optimum variation in the volume concentration of the composite constituents to attain a maximum increase in the ultimate velocity of the sheet. Numerical simulation showed that the optimum structure of the sheet calculated using analytical relations is nearly optimal for different pulse shapes of the accelerated magnetic fields. The possibility of considerably increasing the ultimate velocity through the use of composite layers compared to the ultimate velocities for the homogeneous materials constituting the composite is shown analytically and numerically. For an Fe-Cu-Cu sheet, this increase can reach a factor of two to three.