Abstract: The software GLSPA (GPS level simulation process analysis) was numerically applied to the investigation of the effects of different smooth factors in GPS level/elevation fitting by Hardy function on the fitting precision. The results showed that the fitting precision is improved with increasing smooth factor for forward hyperbolic kernel functions but not for all kernel functions, and there is a maximum of smooth factors for inverse hyperbolic kernel function and the fitting precision lowers if exceeding the maximum. To find out smooth factor that is appropriate to all of relevant kernel functions, lots of analog computation and mathematical statistics were done with the results analyzed to propose first a formula to calculate the smooth factor. The formula is available to solve the problem that the fitting precision is unstable because the smooth factors cannot be determined accurately when fitting the GPS level/elevation by Hardy function.