In tokamak disruptions, the Ohmic current can be replaced by a centrally peaked runaway electron (RE) current, significantly affecting resistive stability. Previous analytical studies have shown that, in the linear phase, the presence of REs enhances the growth rate of tearing modes (TMs) compared to the corresponding Ohmic current case. In the nonlinear regime, RE-driven currents can lead to larger magnetic islands. These results rely on the simplifying assumption that REs propagate at the speed of light and neglect higher-energy effects such as finite orbit width. In this work, we investigate the impact of RE beams with different energies on resistive TMs. A hybrid fluid–kinetic model implemented in the 3D nonlinear MHD code JOREK is employed, in which REs are treated kinetically using a relativistic guiding-center approach, while the background plasma is described by reduced MHD equations. Our results demonstrate that the presence of RE beams significantly modifies the instability characteristics. Specifically, increasing the RE beam energy introduces a stabilizing effect, leading to a reduction in both the linear growth rate and the nonlinear saturation level. This stabilization also suppresses the development of stochastic magnetic regions, thereby reducing particle transport. Furthermore, finite RE energy induces a Grad–Shafranov shift, introducing equilibrium asymmetry that drives toroidal mode coupling and results in more complex nonlinear dynamics. These findings highlight that finite-energy effects of RE beams play a crucial role in modifying resistive instability behavior and associated RE transport processes in plasmas.