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The demand for high-performance computing resources has led to a paradigm shift towards massive parallelism using graphics processing units (GPUs) in many scientific disciplines, including machine learning, robotics, quantum chemistry, molecular dynamics, and computational fluid dynamics. In earthquake engineering, artificial intelligence and data-driven methods have gained increasing attention for leveraging GPU-computing for seismic analysis and evaluation for structures and regions. However, in finite-element analysis (FEA) applications for civil structures, the progress in GPU-accelerated simulations has been slower due to the unique challenges of porting structural dynamic analysis to the GPU, including the reliance on different element formulations, nonlinearities, coupled equations of motion, implicit integration schemes, and direct solvers. This research discusses these challenges and potential solutions to fully accelerate the dynamic analysis of civil structural problems. To demonstrate the feasibility of a fully GPU-accelerated FEA framework, a pilot GPU-based program was built for linear-elastic dynamic analyses. In the proposed implementation, the assembly, solver, and response update tasks of FEA were ported to the GPU, while the central-processing unit (CPU) instructed the GPU on how to perform the corresponding computations and off-loaded the simulated response upon completion of the analysis. Since GPU computing is massively parallel, the GPU platform can operate simultaneously on each node and element in the model at once. As a result, finer mesh discretization in FEA will not significantly increase run time on the GPU for the assembly and response update stages. Work remains to refine the program for nonlinear dynamic analysis.