The general approach to the accurate calculation of the two-dimensional electromagnetic field scattered by a system of infinitely thin and extended perfectly conducting screens in a dielectric slab (waveguide) is suggested. The slab is situated between two semi-infinite homogeneous half-spaces of different electromagnetic properties and is illuminated by two-dimensional E - or H - polarized electromagnetic waves. The cross-section of the screens system is supposed to be arbitrary. The integral equations of the corresponding diffraction problem are derived and the numerical method of solving them is developed. The integral equations kernel contain the usual free-space Green function and the Sommerfeld-type integrals of two variables. The efficient method of the second kernel part evaluation is proposed. Some field calculation results for screens of rectilinear and elliptic cross-section are presented and discussed.