The process of concrete cracking is a common problem because the first micro-cracks due to the loss of moisture may appear even before the concrete is loaded. The application of fracture mechanics allows for a better understanding of this problem. Steel-fiber-reinforced concrete (SFRC) samples with a notch were subjected to a three-point bending test, and the results for crack energy were used to analyze the concrete’s material properties. In this paper, an experimental and numerical analysis of SFRC with rapid changes in the force (F) crack mouth opening displacement (CMOD) curve (F-CMOD) is presented. In order to obtain the relevant F-CMOD diagrams, three-point bending tests were carried out with non-standard samples with a thickness equal to one-third of the width of standard samples. For analysis purposes, crimped steel fibers were adopted. A probabilistic analysis of the most important parameters describing the material in question, such as peak strength, post-cracking strength, crack mouth opening displacement (CMOD), fracture energy, and the post-cracking deformation modulus, was conducted. The tests and the analysis of their results show that the quasi-static numerical method can be applied to obtain suitable results. However, significant dynamic effects during experiments that influence the F-CMOD curves are hard to reflect well in numerical calculations.