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Ribbons with a porosity varying from 22% to conditional 0.5% have been produced by rolling a multilayer knitted-mesh package made of 12Kh18N10T steel wire bundles 30 μm in diameter. Resonant cyclic loading techniques have been employed to plot the experimental dependences of the elastic and damping properties on the porosity and compressive strain of the material. It is shown that the main factor influencing the material’s properties is porosity when it is higher than 5% and plastic strain when porosity is lower than 5%.