The Discrete Element Method (DEM), also known as Distinct Element Method (DEM), is extensively used to study divided media such as granular materials. When brittle failure occurs in continuum such as concrete or ceramics, the considered media can be viewed as divided. In such cases, DEM offers an interesting way to study and simulate complex fracture phenomena such as crack branching, crack extension, crack deviation under coupled mode or crack lip closure with friction. The fundamental difficulty with DEM is the inability of the method to deal directly with the constitutive equations of continuum mechanics. DEM uses force–displacement interaction laws between particles instead of stress–strain relationships. Generally, this difficulty is bypassed by using inverse methods, also known as calibration processes, able to translate macroscopic stress–strain relationships into local force–displacement interaction laws compatible within DEM frameworks. However, this calibration process may be fastidious and really hard to manage. The presented work proposes to improve the Distinct Lattice Spring Model in order to deal with non-regular domains, by using Voronoi cells, which allow to completely fill the volume space of discrete domains. With this approach, the rotational effects must be included in the contact formulation, which enables the management of large rigid body rotations. This work also introduces a simple method to manage brittle fracture. Using non-regular domains avoids the cracks paths conditioning, and allows to reproduce quantitatively the Brazilian test, very popular in the rock mechanics community.