This paper describes the nucleation and propagation of cracks in brittle cellular material. Four basic patterns with triangular, square, hexagonal and kagome-type cells are considered. The cracks propagate by sequential failure of critical elements. The analysis technique hinges on the combined use of the structural variation method and the representative cell method. While the latter allows for the analysis of periodic structures under arbitrary loads, by means of the discrete Fourier transform, the former analyzes modified structures (the cracked lattices) on the basis of analysis of the pristine structure (the periodic lattices). Within the assumptions of Bernoulli-Euler beam theory the suggested method for the analysis of infinite cracked lattices is exact. Although most cracks follow intuitive paths it was found that the microstructure of cellular materials has a significant influence on the crack pattern.