The optimal compositions of fine-grained concrete (FGC) with two-level reinforcement with fiber are determined via the extreme modelling of experimental data based on the Scilab engineering and scientific computing environment. At the macro level brass plated fibre of the wave profile FSW LV 15/0.3 made of steel grade 70-85 with the fiber length of 15 mm and the diameter of 0.3 mm was used for reinforcement. At the micro-level the halloysite nanotubes NN-RTE 200 with the particle sizes from 0.05 to 5 microns were applied. Having calculated the models the designed program Extr.sce determined the extrema of the required characteristics of fine-grained concrete Max_z and their coordinates max_x and max_y, corresponding to the contents of the brass plated fiber (x) and halloysite nanotubes additive (y). The graphic dependences of the compressive strength, bending strength and water absorption of fine-grained fiber concrete on the content of brass plated fibre and halloysite nanotubes additive with minimum, average and maximum cement content in it in the form of contour and 3d graphs of the interpolation surface are obtained. Two-level reinforcement of FGC, optimized by the program Extr.sce, proved that fine-grained concrete with 10% of brass plated fibre, 20% of halloysite nanotubes additives, and cement content of 600 kg had the maximum compressive strength of 70.26 MPa. In order to obtain FGC with maximum bending strength (17.43 MPa), there should be 5% of brass plated fibre, 10% of halloysite nanotubes additives, and 600 kg of cement in it. The fine-grained concrete without any reinforcement additives will have the minimum water absorption (3%).