<p>This paper proposes a finite-time disturbance rejection controller to address the force-tracking performance degradation of aerospace electro-hydraulic load simulators (EHLSs) under large loads, which is induced by inherent nonlinearities, uncertainties, and lumped disturbances. First, an integrated system dynamic model is formulated, incorporating position-coupled disturbances, uncertainties, and lumped disturbances, to explicitly reveal the surplus force generation mechanism and system characteristics. Second, a super-twisting finite-time extended state observer (STFT-ESO) is developed to mitigate control performance degradation caused by asymptotic convergence and residual observation errors inherent in ESOs. Specifically, an adjustment controller is introduced to construct the super-twisting structure, and a global fast terminal sliding mode surface replaces the linear counterpart, enabling finite-time convergence of observation errors to equilibrium. By tailoring its structure to the system dynamics, a system-specific STFT-ESO is further designed to enable finite-time estimation of difficult-to-measure states and lumped disturbances. These accurate estimates are then embedded into the nonsingular fast terminal sliding mode control (NFTSMC) framework to formulate the STFT-ESO-based NFTSMC scheme, guaranteeing system robustness and fast finite-time tracking error convergence. Finally, the finite-time stability of the proposed observer and controller is rigorously proven using Lyapunov theory, and comparative simulations and experiments validate the effectiveness of the proposed methods.</p>