The Global Positioning System (GPS) now makes it possible to define forest boundaries using double differenced carrier phase observables. They are mostly processed with algorithms based on the Least-Squares Estimation (LSE). Although GPS was completely developed for outdoor navigation, sometimes it can be used in near/under tree or building shading. In such a case, before applying the LSE, both the functional and stochastic models should be properly defined in order to obtain reliable positioning. While the functional model for precise GPS positioning is sufficiently well known, realistic stochastic modeling is still a difficult task to accomplish in the case of unfavorable conditions. This paper analyzes the achievable efficiency of the stochastic modeling for the positioning near/under the forest. A static campaign was performed at two surveying sites that have been established near the effect of tree shading. The experiments show the efficiency of stochastic models depending on the forest. It is clear that sigma-e and sigma-A models give optimum solutions for the sites located near the tree canopy. Moreover, weighting procedures based on the C/N0 values can successfully cope with the corruptive effects caused by the tree canopy. As a result, a proper stochastic model for carrier phase observables should be used as an important tool in parameter estimation for handling multipath effect and signal distortion caused by the forest canopy.