The article discusses methods for constructing and research stereometric visual images of multi-criteria alternatives. The difficulty of applying traditional decision-making methods when choosing the best alternative in the case of decision-making tasks with a large dimension is noted. Methods are proposed for reducing the dimension of a decision-making problem by constructing stereometric visual images that describe choice set and criteria set. The tasks of visual analytics are highlighted in the course of reducing the dimension of the decision-making task: grouping and ranking criteria, pairwise comparison and filtering of alternatives. A description of the methods for constructing stereometric visual images of multi-criteria alternatives based on histograms of alternatives and criteria is given. Also describes a method for constructing surface of the criteria's correlation. Using the developed method of alternatives visualization as a single image enables their visual filtering. The application method of the criteria visualization as a single image in combination with the construction and analysis of surface of the criteria's correlation allows for the grouping and ranking of criteria. The experiment is described on the application of the proposed methods for constructing and studying stereometric visual images of multi-criteria alternatives using the example of the problem of choosing the best OpenFoam solver, with the help of which estimates of the accuracy of calculating the inviscid flow around the cone were obtained. It is shown how, due to the above visualization methods, it is possible to reduce the count of criteria by several times. © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).