Computational solid dynamics, which plays an important role in manufacturing and disaster pervention, requires a very high computational cost. As a consequence of this high computational cost, a variety of practical problems remain unsolved. Quantum computer, as next-generation compouting devices, have the potential to address these problems. On the other hand, although some applications in computational mechanics have been verified in recent years, there are few examples for solid mechanics. Therefore, in this study, we propose a aproach to performn transient analysis of simple harmonic motion of elastic structures via Hamiltonian simulation, which is a method to calculate time evolution of the Schrödinger equation form by quantum computer. According to previous study , they show that an oscillator governed by a second-order equation of motion can be simulated via Hamiltonian simulation. However, their method avoids calculating the square root of a matrix—an essential operation—by exploiting properties of the graph Laplacian structure, and thus cannot be directly extended to mechanical problems involving continuous media such as elastic bodies. Proposed method considers the calculation of the matrix square root and spatial discretization by finite element method, then the method is extended to solid dynamics. Using this method, the time-history response of the velocity at each nodes are obtained. The algorithm is implemented consistently using Quantum Singular Value Transformation (QSVT), which provides a unified process for various quantum algorithms, such as the calculation of the matrix square root or Hamiltonian simulation. Within this framework, we examine overall computational complexity and error, while comparing the numerical errors with the corresponding theoretical error bounds. In closing, we discuss the extension to practical problem such as non-conservative systems with damping.