Specific mechanisms underlying the critical velocity in cold gas particle spray applications are still being discussed, mainly due to limited access to in situ experimental observation and the complexity of modeling the particle impact process. In this work, particle bonding in the cold spray (CS) process was investigated by the finite element (FE) method. An effective interfacial cohesive strength parameter was defined in the particle–substrate contact regions. Impact of four different metals was simulated, using a range of impact velocities and varying the effective cohesive strength values. Deformation patterns of the particle and the substrate were characterized. It was shown that the use of interfacial cohesive strength leads to a critical particle impact velocity that demarcates a boundary between rebounding and bonding type responses of the system. Such critical bonding velocities were predicted for different interfacial cohesive strength values, suggesting that the bonding strength in particle–substrate interfaces could span a range that depends on the surface conditions of the particle and the substrate. It was also predicted that the quality of the particle bonding could be increased if the impact velocity exceeds the critical velocity. A method to predict a lower bound for the interfacial bonding energy was also presented. It was shown that the interfacial bonding energy for the different materials considered would have to be at least on the order of 10–60 J/m2 for cohesion to take place. The general methodology presented in this work can be extended to investigate various materials and impact conditions.