There is different robust estimation methods used for detecting small gross errors which may be presence in geodetic observations. Some of these methods are robust M-estimators, Least Absolute Sum and Danish method. The conventional Least Squares Estimation method and these robust estimation methods have been tested and applied on a precise geodetic network designed for detecting earth’s crustal deformations using singlepoint and rigid body displacement models. The results show that, the method of least squares leads to biased, unfavorable solution and useless estimates if the singlepoint displacement does not taken into considerations in the solution’s mathematical model. In contrast, the results of robust estimation methods are attained unbiased in a single estimation step. A reliable separation of single-point displacement and the general deformation model is achieved without difficulties. The comparison of results proved that, the Danish method gave the most accurate results. It also was more sensitive to outliers which may be presence in surveying observations in case of applying single-point displacement model. The Least Absolute Sum method was very nicely reproduces the simulated deformations and does not show a contamination of the estimated positions of stable points in the case of rigid body displacement model. The results of adjustment using rigid body displacement model were not identical with the nearly correct results of single-point displacement model. So, the rigid body displacement model may be not suitable for geodetic networks.