Abstract: An attempt is made to solve radically the key problem on evaluating the cylindricality error with sampling points in rectangular spatial coordinates. According to the definition of cylindricality error as specified in the national standards, a mathematical model was developed to evaluate the cylindricality error by least square method, to which the origin of coordinates can be randomly selected and no isogonal requirements for sampling points. The simulated results are found highly coincident with the calculated results by the model, and the error arising from the model is negligible. Based on the model, the cylindricality in conformity with minimum conditions can be calculated by way of four-dimensional non-restraint optimization algorithms. The model can be used on either measuring machines with rectangular spatial coordinates or other intelligent measuring instruments.