In the practical application of three coordinates measuring machine, only the estimated value of the measurement result is given without the measurement uncertainty. So this measurement result is incomplete. Measurement uncertainty can be divided into method uncertainty and implementation uncertainty. Generally method uncertainty is zero in default state, and implementation uncertainty is induced by measuring instrument or measurement environment. The mathematical evaluation model of the roundness error was given based on least squares method (LSM). According to ISO guide to expression of uncertainty in measurement (GUM), the influencing factors on implementation uncertainty were analyzed and the transfer function of error influencing factors for implementation uncertainty was deduced. Then uncertainty components of various factors were obtained. As a result, the synthesis implementation uncertainty was acquired finally. Adaptive Monte Carlo computer simulation（MCM）was adopted to verify the effectiveness and the application scope of GUM from quantity of measuring points, standard uncertainty, estimated value of roundness error, and left & right endpoints of shortest coverage interval. 