Miniature power semiconductor devices mounted on printed circuit boards (PCBs) are normally cooled by means of PCB vias, copper pads, and/or heatsinks. Various reference PCB thermal designs have been provided by semiconductor manufacturers and researchers. However, the recommendations are not optimal, and there are some discrepancies among them, which may confuse electrical engineers. This paper aims to develop analytical thermal resistance models for PCB vias and pads, and further to obtain the optimal design for thermal resistance minimization. First, the PCB via array is thermally modeled in terms of multiple design parameters. A systematic parametric analysis leads to an optimal trajectory for the via diameter at different PCB specifications. Then, an axisymmetric thermal resistance model is developed for PCB thermal pads where the heat conduction, convection, and radiation all exist; due to the interdependence between the conductive/radiative heat transfer coefficients and the board temperatures, an algorithm is proposed to fast obtain the board-ambient thermal resistance and to predict the semiconductor junction temperature. Finally, the proposed thermal models and design optimization algorithms are verified by computational fluid dynamics simulations and experimental measurements.