In this study, we develop a quantum computational framework for the simulation of an axially deformed bar, a canonical problem in structural mechanics. Motivated by the potential of quantum computation to accelerate numerical analyses based on partial differential equations, increasing attention has been directed toward the application of quantum algorithms to engineering simulations. Despite the versatility of Quantum Eigenvalue Transformation (QET) as a theoretical foundation for quantum algorithms, the concrete realization of block encoding and its evaluation at the quantum circuit level remain insufficiently explored. We consider the tensile deformation of a bar as a prototypical engineering problem and develop a circuit-based quantum simulation grounded in QET through a concrete example, aiming to bridge classical structural analysis and quantum circuit implementations. The axial deformation problem is formulated within the framework of the finite element method and discretized into a linear system characterized by a sparse stiffness matrix. Leveraging structural properties of the stiffness matrix, including sparsity and symmetry, an efficient block encoding circuit is constructed. The inverse operation of the stiffness matrix is then realized on a quantum circuit via QET, and the resulting quantum state is systematically examined for consistency with the corresponding classical solution. To assess the feasibility of the proposed approach, numerical simulations are performed under finite-dimensional settings. The accuracy of the constructed quantum circuits is quantitatively evaluated, together with explicit estimates of quantum circuit complexity and approximation errors induced by QET. The results indicate that the proposed framework reliably reproduces the expected behavior of the axial deformation problem within a prescribed tolerance, while clarifying the computational cost and error characteristics inherent to the quantum circuit implementation.