Recent experimental observations of anisotropic conductivity in stretched polymer electrolyte films of the poly(ethylene oxide) family are discussed. The main experimental observations, enhancement of the ionic diffusion and conductivity in the stretch direction, and decrease in these transport coefficients in the normal direction are interpreted in terms of an effective two-phase model. This two-phase model is based on the idea that a highly conducting phase is associated with oriented molecular structures which are surrounded by poorly conducting boundary regions. This model is evaluated within the framework of differential effective medium theory (DEMT). Under stretching these regions change from spherical to prolate-spheroidal shapes. The computed dependence of the DC conductivity tensor and its AC counterpart on the stretch parameters is in good agreement with experimental results.