This article addresses the study of crack behavior elicited on axial fatigue in specimens joined by butt weld made of steel ASTM A36 by using fracture mechanics and simulation software of finite elements (Ansys APDL, Franc3D). The computational model was initially to define the geometry model by using CAD software. Specimens with Weld Reinforcement of 2 mm and 3mm were simulated. Subsequently, the type of element for the mesh, the information inclusion concerning material mechanical properties and load conditions were selected. By using Franc3D software, the crack propagation phenomenon is analyzed, and its growth parameters have been established. In this way, it is possible to calculate the magnitude of stress intensity factor (SIF) along the crack front. It is concluded that the stress located in the weld toe is maximized proportionately to the size of the weld reinforcement due to the concentration effect of geometric stress. In addition, it is observed that the propagation rate obtained from Paris law has a similar behavior for the studied weld reinforcements; the latter as there were short cracks.