In this paper we describe the program of triangular mesh construction with Delaunay properties for the domains, which boundaries consist of straight lines and arcs of circles and ellipses. There was used the geometric preprocessor TTNS in order to form the discret similarity for the calculated domain and to construct its finite-difference approximation. This preprocessor produces the representation of mesh domain not as some knots variety, but as a variety of mesh lines segments, completely belonging to the domain, with the final points on the boundary. So, it is possible to reach a linear dependence of computational time and memory required on the mesh-size parameter because of the way of final data representation: it is O(h-1) value.

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