For the study of fracture criteria, adhesive tensile strengths (σ_Y) of scarf joints with a scarf angle of 30^o and butt joints bonded by a brittle epoxy adhesive A and a ductile epoxy adhesive B have been measured at adhesive layer thickness (h) from 0.05 to 5.0 mm, and three-dimensional elastic finite element analyses have been performed. σ_Y of each joint decreased with an increasing value of h. A brittle fracture occured on the scarf and butt joints bonded by adhesive A and the butt joints bonded by adhesive B. The fracture of scarf joints A and B satisfied a maximum principal stress criterion and the von Mises criterion, respectively. Gradients of σ_Y-h curves for butt joints A and B were greater than those predicted from the results of stress analyses. The location of fracture initiation and fracture modes of adhesive layers observed with an optical microscope agreed with those expected from the results of experiments and stress analyses.