Firstly, different concrete beams reinforced by basalt fibers, polypropylene fibers, hybrid fibers and silica fume were experimentally tested for their cracking moments. The plastic deformation development coefficient k of each concrete beam was calculated based on the tested cracking moments and the measured material properties. Then the stress distributions of the tensile concrete subjected to cracking were described. After that, the plastic influence coefficient of the cross section resistance moment corresponding to each beam could also be calculated using k. Lastly, the cracking moment formulas for basalt or polypropylene fiber reinforced concrete beams were deduced based on the plastic influence coefficient. The analysis results indicate that the plane cross section assumption is basically satisfied for fiber reinforced concrete beams. The addition of fibers and silica fume increased the cracking moments of the concrete beams. The basalt fibers show better performance than polypropylene fibers under an identical volume fraction. Moreover, the coefficient k provides a reference for the theoretical deduction of the cracking moments of fiber reinforced concrete beams. It can be used as an index to evaluate the plastic deformation ability of tensile concrete subjected to cracking. The splitting tensile strengths, as well as the plastic deformation ability of tensile concrete, affect the cracking moments of concrete beams. The proposed formula for the cracking moments of basalt or polypropylene fiber reinforced concrete beams can be used as reference for relevant calculation.