A new class of functions - "FLOZ- functions" (Functions of LOcal Zeroing out), which makes it possible to form the zero domain of a scalar-valued multidimensional function of complex configuration by means of R-functional modelling is considered. We represent the solution of the inverse problem of analytical geometry for a non-convex contour construction obtained by V.L. Rvachev’s mathematical apparatus of R-functions. The problems of constructing an algorithm for automation the proposed by V.L. Rvachev solutions are described. Presented arguments show the complexity of constructing an algorithm based on recursive attachment. The functional voxel model was created in the RANOK 2D system. An approach to the function of local zeroing out (FLOZ-function) construction for the general (multidimensional) case is described. A two-dimensional function of local zeroing out is selected for solving the problem of a non-convex contour constructing. It is shown that the function of local zeroing out allows to create the sequential algorithm of automation the non-convex contour construction. Examples of automation the considered problems of V.L. Rvachev to the nonconvex contour construction are given. The function of local zeroing out for three-dimensional space (3D FLOZ-function) is considered. An example of functional voxel modelling of a 3D sphere model based on a triangulated network consisted of 80 triangles is given.