The mechanical behavior of hollow blocks made of concrete and natural sisal fibers tested to failure is dealt with. First, the results of compression tests carried out on blocks, prisms and wallettes are presented; for comparison, the mechanical response of companion plain concrete specimens is also shown. Then, a numerical model is developed to simulate the nonlinear behavior of the blocks, with the aim of predicting the possible crack growth of structural masonry elements in the design phase. The parameters and the boundary conditions that define the models are calibrated to match the experimental load-displacement curves. A qualitative description of the damage evolution in the elements using the smeared crack model implemented in the commercial FE program DIANA and the XFEM implemented in Abaqus is obtained. The experimental and numerical results are critically discussed, and possible future improvements of the proposed models are outlined.