The rivet joint is an important mechanical connection for hot structures made of ceramic matrix composites. The development of chemical vapor infiltration technology provides a possible application of novel rivets for these structural components. However, connectors can still be the weakest link for structural integrity due to the severe stress concentration around the rivet joint holes. The geometry parameters of the rivet hole can be key influencing factors to the structural strength. A comparative evaluation is presented to analyze the influence of opening-hole shapes on the structural stress concentration of a composite plate. The opening-hole shapes considered include circle, ellipse, and racetrack. The finite element (FE) models of specimens with the three shapes of rivet holes were constructed. The stress distributions of the specimens under tensile loading were analyzed to compare the stress concentration factor (SCF) of different opening-hole shapes. An optimal shape, i.e. racetrack-shaped, was determined based on the SCF reduction of specimen-level comparison. Then, FE models of a composite plate containing rivet holes were built to verify the outperformance of the racetrack-shaped hole. A stress concentration reduction of the plate with racetrack-shaped holes was observed compared to the one with circular holes.