This work presents a novel numerical model to simulate the failure process in masonry structures subjected to static loads via finite element method. Brick and mortar joints are modeled separately with their own constitutive equations. Interface finite element with high aspect ratio are used to simulate the mortar interface and inserted by the mesh fragmentation technique. The main advantage of this strategy is supported by the fact that, as the aspect ratio of a standard low-order solid finite element increases, the element strains also increase, approaching the same kinematics as the Continuum Strong Discontinuity Approach. A constitutive model was developed, based on the continuum damage mechanics, in order to represent the behavior of the interface finite elements. This model is able to simulate the creation and propagation of cracks, as well as, the frictional effects in dependence on stress confinement on the interfaces. Furthermore, as the objective of this work aims to simulate the failure in the mortar joints, the brick elements are assumed as linear elastic material. Three node standard triangular finite element are used to represent the bricks. Several numerical models are carried out. Initially, basics tests are show in order to demonstrate the main characteristics of the proposed model subjected to tensile, compression and shear loads. Subsequently, masonry structures are subjected to static loads are analyzed and the results compared with the experimental responses in order to validate the proposed model. This technique proved to be very promising for the simulation of failure onset and propagation in mortar joints of masonry structures.