The article describes methodological, scientific and practical approaches to modern 3D modeling, which are based on the application of algebraic R-functions. To create 3D objects the method of functional-voxel modeling is used, which is successfully applied to a wide variety of tasks in the geometric formulation. Model creation is divided into three stages. The initial stage of creating a 3D model is its description in a specialized programming language. With the help of this language it is possible, using the V.L. Rvachev’s functions – R-functions, to define complex and manifold geometric shapes and operations quite easily. The second stage of model creation is its "growing" in the form of voxels, the number of which depends on the degree of required accuracy of the model, its partitioning. Here, the calculation of geometry using parallelism and shader programs on the GPU. The final stage is the visualization of the resulting models in point, voxel and smooth geometric form. The development of such a system of modeling and visualization of 3D objects will expand the horizon of solutions in the field of modern robotics, forecasting under uncertainty, as well as life cycle support systems in industrial production.