This study investigates the effects of adding different types of fibers to concrete mixes on the shear behavior of double-span fiber-reinforced concrete beams with or without shear reinforcement. As a part of the experimental study, a total of twenty-seven natural-scale double-span beams were tested. The beams, made of concrete with steel or basalt fiber, with fiber dosages of 78.5 and 5 kg/m3, were tested under shear force. The three tested series consisted of three beams with dimensions of 120 × 300 × 4150 mm, with various numbers of stirrups and contents of fiber reinforcement. During the tests, the shear capacity of the elements was determined. The values of support reactions, deflection in the middle of the span of both beam spans, deformations on the surface of the concrete member in the middle of the span in the compressive and tensile zone, and cracking (crack development and crack width) were also measured. The beams were tested using a digital image correlation (DIC) technique. Test results show that shear capacity increases in beams made of concrete with steel (1.87) or basalt fibers (1.23). Moreover, the failure mode changes from shear (brittle) to flexure-shear (less brittle). The experimental shear capacity of beams was compared with the theoretical values predicted by different design codes, i.e., fib Model Code 2010 and RILEM TC 162-TDF 2003. The results show that all the design codes underestimate the contribution of fiber-reinforced concrete beams to shear resistance and greatly overestimate the contribution of shear reinforcement.