Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields. However, high precision is still one of the challenges when they are used for advanced machine tools. One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations, especially at high speeds and under heavy loads. A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process. Based on the dynamic model constructed by the Newton-Euler method, all the inertia loads and constraint forces of the links are computed and their deformations are derived. Then the kinematic errors of the machine are derived with the consideration of the deformations of the links. Through further derivation, the accuracy of the machine is given in a simple explicit expression, which will be helpful to increase the calculating speed. The accuracy of this machine when following a selected circle path is simulated. The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated. The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine. The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.