Fibre-reinforced concrete (FRC) has gained tremendous attention in many disciplines due to its high initial strength, favorable mechanical properties, structural lightness, and energy-absorbing properties. In this research, Barchip fibres, Forta, and Basalt are utilized to reinforce concrete under penetration effect loading to examine the energy absorption and impact strength characteristics. To determine the parameters of the percentage of fibres on the impact resistance properties, the Box–Behnken method as a subset of the response surface method (RSM) was used. A diagram of RSM is adopted to determine the optimal percentage of fibres for higher initial strength and energy absorption. Results obtained using Design-Expert software revealed an initial strength of 886.127 N and an optimal energy absorption of 4.9865 J. In addition, the calculated R2 values and normal probability graphs showed a fairy accurate correlation between the results of the experimental and mathematical approaches. Finally, this study evaluated the fracture surface, adhesion of the fibres to the concrete, and degradation modes of the fibres to pave the way for optimal utilization of these hybrid FRCs.