To prevent the problem of test chance in solid wood furniture joint strength testing and reduce the destructive test and test costs, the finite element method (FEM) and ABAQUS software were used to establish a cohesion model, which can predict the pull-out strength of L-shaped and T-shaped members using round tenon joints in the presence of adhesives. In addition, the effect of the diameter of the round tenon on the pull-out strength of the joints was investigated. The simulation results revealed that with the increase in the diameter, the pull-out strength of the double round tenon joint increased, indicating that the diameter of the round tenon is a key factor that affects the pull-out strength of joints. Furthermore, errors between the finite element analysis (FEA) results and the average test results of two members with different diameters were less than 15%, and the cloud diagrams of the structural stresses were consistent with the test results. Therefore, the established FEM is confirmed to be accurate and suitable for predicting the pull-out strength of designed round tenon joints in solid wood furniture. This paper provides new ideas and methods for the non-destructive testing of the structural-mechanical properties of solid wood furniture.