An accurate and efficient numerical solution is presented for the two-dimensional electromagnetic wave scattering from multilayered resistive strip gratings. Both E- and H-waves are treated. The method is based on the integral equations combined with the moment method with regularization procedure. The numerical experiment reveals the criteria for the truncation numbers. The reflected, transmitted, and absorbed powers are computed for various grating parameters and frequencies. Special attention is paid to maximizing the absorption into the strips, and thereby the relative absorbed power amounts to more than 90%.