This study investigates the tensile behavior of pultruded composite square tubes with single- and double-bolt joints to evaluate their ultimate load-bearing capacity and failure modes. A series of experiments was carried out to examine the effects of hole size, edge distance, and the presence of a reinforcing gasket on joint performance. The results indicate that incorporating a multiaxial fiber-reinforced resin matrix composite gasket significantly enhances joint strength, achieving up to a 295% increase in bearing capacity. In single-bolt configurations, reducing the edge distance improved the effectiveness of the gasket, leading to higher ultimate strength, as it enhances the lateral confinement of the gasket. For double-bolt joints, a shorter spacing between holes further amplified the reinforcing effect of the gasket under constant hole size and edge distance. A theoretical model was developed to estimate the ultimate load, and the calculated results showed strong agreement with experimental observations. Numerical predictions showed a strong correlation with experimental findings, confirming the model’s reliability and accuracy.