Concrete is a widely used material in various industries, including hazardous waste management. At the same time, its production creates a significant carbon footprint. Therefore, intensive research is being conducted to create more eco-friendly concrete, for example, partially replacing cement with by-products such as oil shale ash (OSA) or improving properties by adding dispersed fibers such as basalt fibers (BFs). The article consists of experimental testing of nine types of concrete and the modeling of crack propagation in bending. The basic trends of crack propagation in samples of concrete with OSA and BFs are simulated using a two-dimensional Finite Element (FE) model considering only material degradation on the opening crack surface and experimental data of three- and four-point bending tests. Crack propagation is modeled using the bridging law approach. A surrogate model for predicting the peak loading as a function of tensile strength and fracture work was created. An examination of the results of the FE model shows that the bilinear and nonlinear bridging law functions best describe the crack growth in the analyzed material. A comparison of experimental and modeled results showed that the length of the composite BF strongly affects the accuracy of the numerical model.