This article presents research on the bearing capacity and methods of calculating reinforced concrete beams on the shear without internal shear reinforcement, which are strengthened with a composite FRCM system. The test samples were divided into two series: the first series—control, in which the variable parameter was the shear span (a/d = 2, a/d = 1.5, and a/d = 1); and the second series—reinforced by the FRCM system, without load, and strengthened at different load levels. The method of calculating experimental beams was tested according to the current code and data from the fib report. In this article, recommendations for determining the angle of inclined struts θ, the coefficient of the concrete shear strength CRd,c, and the coefficient of the load level at which strengthening is performed are proposed. The calculation with the these recommendations showed a good convergence of experimental and theoretical data in the 16–29% range, which is a much higher convergence than the calculation without these recommendations.