This work incorporates newly introduced Lattice Discrete Particle Model (LDPM) to assess the failure mechanism and strength of hollow concrete blocks. Alongside, a method for the graphical representation of cracked surfaces in the LDPM is outlined. A slightly modified calibration procedure is also suggested and used to estimate required model parameters for a tested concrete sample. Next, the model is verified for a compressively loaded hollow block made of the very same concrete. Finally, four geometries commonly used in the production of hollow concrete blocks are selected, numerically simulated, and their failure properties are explored under concentric and eccentric compressions.