A 3-D nonlinear finite element code was established to assess the effects of the fiber orientation angle of the laminates on the stress distributions and the failure prediction in single lap joints (SLJs) subjected to uniaxial tensile loading. Eight different configurations were considered and the unidirectional prepregs were laid up in quasi-isotropic ([90/+/- 45/0](2s) and [90/+/- 30/90](2s)), cross-ply ([0/90](4s) and [30/60](4s)), angle-ply ([45/-45](4s) and [55/-55](4s)), and unidirectional ([0](16) and [90](16)). The composite adherends (AS4/3501-6) were assumed to behave as linearly elastic materials while the adhesive layer (FM 73) was assumed to be nonlinear. The nonlinear geometric deformations of the SLJs were also taken into account. The first step in the analysis, a complete 3-D stress analysis, is carried out with a special importance for the evaluation of out-of-plane stresses. Then, the failure index distributions are calculated by using the Tsai-Wu failure criterion for composite adherends and the extended Drucker-Prager failure criterion for the adhesive layer. Consequently, it is seen that the state of stress in the vicinity of the free edge of the joint is fully 3-D which has not been taken into account in any classical theory so far and the normal and shear stress distributions are extremely sensitive to these 3-D effects (anti-clastic, free edge, and bending-twisting coupling effects). Hence, in real applications of adhesively bonded composite joints, the out-of-plane stresses and 3-D effects cannot be neglected and a 3-D finite element method is essential to evaluate explicitly the stress and failure states. Also, for both the adherends and the adhesive layer, the ply stacking sequence has a significant effect on the stress distribution and the failure.