An accurate and efficient numerical solution is presented for a two-dimensional electromagnetic wave scattering from a multilayered resistive strip grating embedded in a dielectric slab. Both E- and H-waves are treated. The problem is formulated into a set of integral equations, which is solved by the moment method accompanied by a regularization procedure. The resultant set of linear algebraic equations has the form of the Fredholm second kind, and therefore yields stable and accurate numerical solutions. The power distribution is computed for several grating parameters. Attention is paid to seek a set of parameters that maximizes absorption in the strips. The low frequency approximate formulas are also derived. This analysis would be useful in designing electromagnetic wave absorbers.