Abstract: A new method was presented to predict the effective elastic constants of unidirectional continuous fiber reinforced composites containing voids of various characteristics based on the similarity between the deformation of the fibers around the voids and the flow field around the 3D Rankine oval. A finite element model of the representative volume cell was proposed, in which the volume fraction change of the fibers around the voids was described by the velocity variation in the flow field, and the direction of the fibers around the voids was described by the streamline shape. The periodic boundary conditions were used to calculate the laminar elastic properties, combining with the probability distribution model of the void shape and the stiffness volume average method. The numerical results agree reasonably with the available experimental data, which validates the computational method in the prediction of the voids influence on the elastic properties of the unidirectional continuous fiber reinforced composites.