According to the uniform and random distribution of fibers, a representative volume element finite element model of uniform and random distribution of filaments was established by the Poisson disk sampling method. Then, a periodic boundary displacement constraint equation was proposed for the aperiodic mesh of the representative volume element finite element model. The displacement difference caused by the mesh node offset was added to the displacement constraint equation based on the traditional periodic displacement constraint equation. Finally, the engineering constants of the representative volume element model were predicted by axial tensile and shear deformation, and the accuracy of the model was verified by comparing the predicted results with the theoretical results. The proposed method in this paper provides a new research method for the prediction and research of braided composite structure performance.