Abstract: A solution to the key problem of evaluating coaxial error in rectangular coordinates was provided. According to the definition of coaxial error as given in Chinese National Standard, a mathematical model based on least square method was developed to evaluate coaxial error, where the origin of coordinate could be selected randomly, and all sampling points were not required at intervals of equal angle. The simulation results indicated that the model is theoretical correct and practical, based on which the coaxial error to meet the requirement for minimum can be directly computed by way of the 4-D non-restraint optimization algorithm. The model can be used for either the 3-D coordinate measuring machines or other intelligent instruments for parts measurement.