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This paper examines the beneficial effects of the spanwise flexibility of the caudal fin for the improvement of the swimming performance for small fishlike robots. A virtual swimmer is adopted for controlled numerical experiments by varying the spanwise flexible trajectories and the spanwise flexible size of the caudal fin while keeping the body kinematics fixed. 3-D Navier-Stokes equations are used to compute the viscous flow over the robot. Elliptical, parabolic and hyperbola trajectories are chosen to describe the spanwise flexible profile of the caudal fin. According to the sign (positive or negative) of the phase difference of the swinging motion, the spanwise flexibility can be divided into the fin surface of bow and the fin surface of scoop. It is observed that for both the fin surface of bow and the fin surface of scoop, the spanwise elliptical trajectory has the optimal swimming velocity, thrust, lateral force, and efficiency. With comparisons, using the flexible caudal fin with the fin surface of bow, the lateral force and the power consumption can be reduced effectively and the swimming stability can be increased while reducing little the swimming velocity and thrust. Meanwhile, using the flexible caudal fin with the fin surface of scoop can greatly improve the swimming velocity, thrust, and efficiency while increasing part of the lateral force and the power consumption. Three-dimensional flow structures clearly indicate the evolution process around the swimming robot. It is suggested that the fish, the dolphin, and other aquatic animals may benefit their hydrodynamic performance by the spanwise flexibility of the caudal fin.