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We introduce GausSim, a novel neural network-based simulator designed to capture the dynamic behaviors of real-world elastic objects represented through Gaussian kernels. We leverage continuum mechanics and treat each kernel as a Center of Mass System (CMS) that represents continuous piece of matter, accounting for realistic deformations without idealized assumptions. To improve computational efficiency and fidelity, we employ a hierarchical structure that further organizes kernels into CMSs with explicit formulations, enabling a coarse-to-fine simulation approach. This structure significantly reduces computational overhead while preserving detailed dynamics. In addition, GausSim incorporates explicit physics constraints, such as mass and momentum conservation, ensuring interpretable results and robust, physically plausible simulations. To validate our approach, we present a new dataset, READY, containing multi-view videos of real-world elastic deformations. Experimental results demonstrate that GausSim achieves superior performance compared to existing physics-driven baselines, offering a practical and accurate solution for simulating complex dynamic behaviors. Code and model are available at our project page: https://www.mmlab-ntu.com/project/gausim/index.html .