The efficient evaluation of Sommerfeld integrals (SIs) in planar layered media has been a long-term bottleneck in the accurate electromagnetic analysis of modern radio frequency (RF) circuits, chips, and devices. This work investigates the high-performance computing of SIs using modern graphics processing units (GPUs) to alleviate this difficulty. Based on the numerical integration procedure with controllable accuracy for SIs, the GPU parallel schemes for SI heads and SI tails are first presented. By eliminating the redundant calculations in SI of multiple frequencies, highly efficient parallel computing enhanced by tensor cores of GPU is developed, and it evaluates the multiple frequency SIs simultaneously. In addition, the mixed-precision computing that further accelerates computing is also studied and tested. Extensively numerical experiments are carried out on two commercial gaming GPUs and verify the performance of the proposed parallel scheme. It achieves a dozen to hundreds speedup compared to that using two high-end CPUs with full OpenMP parallelization.