A new analytical-numerical method based on singularity extraction is presented for efficient and accurate evaluation of one of the reflected Sommerfeld integrals over multilayered media backed by a conducting (PEC) plane. Method is based on extraction of all the poles of the integrand. The method is demonstrated on one element of the tensor multilayered Green's function, where only the singular part of the integrand, i.e. the reflection coefficient, is taken into consideration, as the cause of the largest calculation difficulties. It was also shown that the method practically eliminates all the branch cut singularities except for one.