This book is devoted to generating of non-periodic structures of two-fibre composite material. The first part deals with the well-known principles and laws of random processes. The whole introductory part tends to the application of random processes to the composites, e.g. anizotropy or spatial correlation. The most frequently used and well-known algorithms for generating non-periodic patterns are presented here. Next, the description of inner microstructure is discussed together with the methods of detection of complete spatial randomness. The theoretic part ends with detailed description of four algorithms developed by the author for generating random structures with non-constant diameters of fibres. In the second computational part the comparison of simulated samples obtained by new algorithms and real ones is presented. This comparison is made by mean of techniques of a descriptive statistic. Moreover, the assumptions of normality and homogeneity of samples are checked. These assumptions are usually necessary for next computations, e.g. ANOVA. In conclusion, the obtained results are summarized and the simulated samples generated by different algorithms are compared.