A theoretical framework is presented to describe the optical properties of polarizers produced by tensile deformation of semicrystalline polymers containing dichroic dyes. In the model it is assumed that orientation of both the host polymer and guest molecule occurs in the affine mode. The development of optical anisotropy with orientation is described using an aggregate model. The theory is employed to evaluate the optical characteristics of the polarizers, i.e., dichroic ratio, order parameter, polarizing efficiency, and single-piece transmittance. Good agreement is observed between theoretical predictions and experimental data produced in this work on oriented linear polyethylene/Sudan Red polarizing films. It is shown that the model is useful to estimate the limiting polarizing efficiency and single-piece transmittance of the polarizing films at hand.