A method to evaluate statistical estimation error of the mean of the local average (LA) of a geotechnical parameter is applied to an embankment stability problem. It is known that the LA of a soil mass that contains the critical slip surface controls the stability of an embankment on soft ground. Thus the statistical estimation error problem is specified as the estimation error evaluation problem of this LA mean. The soil profile is model by a stationary random field (RF), which is simplification and idealization of the real ground. The LA at an arbitrary point in the RF is estimated from limited samples obtained from the same filed. The two estimation methods are proposed, namely the General estimation and the Local estimation. The relative position of samples and of the structures are not considered in the former, whereas they are considered in the latter. The theory is illustrated by an embankment stability example.