The proposed procedure of integral mapping is based on calculation of evaluation functions on the integral indicators (II) taking into account the feature of the local geographical environment, when geosystems in the same states in the different environs have various estimates. Calculation of II is realized with application of a Principal Component Analysis for processing of the forest database, allowing to consider in II the weight of each indicator (attribute). The final value of II is equal to a difference of the first (condition of geosystem) and the second (condition of environmental background) principal components. The evaluation functions are calculated on this value for various problems of integral mapping. The environmental factors of variability is excluded from final value of II, therefore there is an opportunity to find the invariant evaluation function and to determine coefficients of this function. Concepts and functions of the theory of reliability for making the evaluation maps of the hazard of functioning and stability of geosystems are used.