Constructive methods and algorithms of stochastic modeling of physical-mechanical fields are proposed based on the theory of R‑functions and fuzzy logic, which allow to take into account technical and technological tolerances for geometric and physical information, measurement errors, rounding errors, and based on the analysis of their complex influence on the development to draw an expert opinion. When solving boundary-value problems of mathematical physics and creating systems for the study of fields of different physical nature, it is important to take into account technical and technological tolerances for geometric and physical information, errors of measurement of physical quantities and errors of rounding. In this regard, there is a need to develop field calculation systems in order to obtain permission for the solution and for further expert judgment. Calculations in existing field calculation systems tend to be deterministic, but in the meantime, real processes are to some extent stochastic, with some imprecision. In order to take this fuzzy into account, it is advisable to transform the existing scheme of physical field research so that, as a result of multivariate computation, a more accurate "fuzzy" solution will be obtained that is closer to reality. It is necessary to enter into the scheme the decision of tolerance, that is, sources of fuzziness, which have the greatest influence on the resultant decision. Practice shows that there are usually three such sources: model tolerances, method errors, and rounding errors. It is necessary to establish the effect of the solution of variation of these values within the tolerances and to explore the possibility of constructing tolerances for this solution. In this regard, it is of great interest to develop systems for the study of physical and mechanical fields that are oriented towards multivariate solution of boundary value problems to account for the variation of the values under consideration within the specified tolerances. The relation between the theory of R‑functions and fuzzy logic is investigated. It is proved that with the necessary generalization of the laws of contradiction and the exclusion of the third set of functions of fuzzy logic coincides with the set of conditional R‑functions. It is shown that functions of logic algebra are concomitant for conditional R‑functions and the set of conditional R‑functions is functionally closed. Based on the results of research in the theory of R‑functions and fuzzy logic, methods and algorithms for modeling fuzzy domains of complex form have been developed. Fuzzy field models and structures of fuzzy solutions are developed, the method of their realization is offered.