The analysis for the electromagnetic radiation or scattering from a material cylinder in the presence of a wedge with impedance faces is presented. The problem considered is two dimensional where the incident field is polarized TM or TE to the axis of the wedge, and the material body may be of arbitrary shape and inhomogeneous. An integral equation is formulated where the field inside the material cylinder is the unknown quantity to be determined and the Green's function for the impedance wedge is included in the kernel of the integral equation which accounts for the presence of the wedge. The integral equation is then solved using a method of moments technique. Employing the specialized Green's function for the impedance wedge reduces the number of unknowns in the moment method matrix since unknowns are only required over the region of the material cylinder and not along the boundaries of the wedge. The primary application for this analysis is to study methods for reducing the EM scattering from wedge shaped objects; specifically the fields which diffract from the sharp corner formed by the edge of the wedge. Attaching a lossy material body to the tip of the wedge is an effective method for reducing these diffracted fields. Optimization techniques are also employed to design the loss profiles of the material bodies in order to maximize their performance for scattering reduction.