Signal integrity (SI) issue is a critical concern as the data rate continues to increase and SI analysis is heavily dependent on simulations. Inaccurate simulation data may result in inadequate design decisions influencing high-speed digital design and optimization. The surface impedance boundary condition (SIBC) concept is generally utilized in commercial electromagnetic (EM) solvers, which is considered to be an efficient technique as the interior region of the conductor of interest does not need to be included in the numerical procedure. The first-order SIBC has been incorporated into many EM simulation tools widely used in industries. In this paper, the limitations of the first-order SIBC in 2D simulations for PCB transmission lines are analyzed and demonstarted for the first time. Different PCB transmission lines with various cross-sectional geometries are simulated in a commercial 2D EM solver with and without the implementation of the first-order SIBC to reveal the effect on the simulated transmission line behaviors. It is found that the accuracy of the simulations with the first-order SIBC decreases as the edge of the signal conductor in the cross-section becomes narrower. The possible solutions are proposed to overcome the issue.