To further improve the joint strength and identify the potential failure behavior of self-piercing riveted (SPR) steel/aluminium hybrid joints under shear and cross-tension loading conditions, a simplified 2D-to-3D simulation process chain is proposed. The finite element models (FEM) for the failure process of SPR joints are established in LS-DYNA and verified against experimental results. The effects of rivet strength, sheet material and thickness, and riveting direction on the joint strength and failure behavior of SPR joints are investigated. The results show that when the rivet strength is less than 1.3 GPa, increasing the rivet strength can improve the joint strength of AS joints under shear load and SA joints under cross-tension load. The joint strength of two types of SPR joints increases gradually and then decreases with an increase in thickness ratio Rt. When the steel/aluminium sheet thickness ratio Rsa exceeds 1.47, the aluminium-to-steel direction should be chosen. Increasing material strength can improve the joint strength of two types of SPR joints, while their sensitivities to the material strength vary under different loading conditions. The sheet material, sheet thickness, and riveting direction can change the failure behavior of the joints, while the rivet strength does not alter the failure behavior. This work contributes to understanding the mechanism of joint strength improvement and enhances riveting quality in industrial practice.