Purpose <p>Motivated by the critical limitation of existing approaches such as error accumulation in time-stepping scheme, exponential growth of ill-conditioned matrix in space-time formulations, and mesh-generation in conventional mesh-based methods, this paper establishes a method combining the meshless backward substitution method with the fast Fourier transform algorithm to construct a hybrid frequency domain framework for solving transient elastic wave propagation problems.</p> Methods <p>First, transient excitations in the time domain are converted to the frequency domain via the fast Fourier transform. Subsequently, the improved backward substitution method is employed to efficiently solve the problems in frequency domain. Then, the transient time-domain response is reconstructed through inverse discrete Fourier transform. To mitigate the inherent boundary truncation artifacts in the conventional fast Fourier transform, a symmetric extension technique is implemented by mirroring the original signal at temporal boundaries. This approach effectively suppresses waveform distortion caused by the spectral leakage. </p> Results <p>Numerical experiments demonstrate the alignment between the computational results and the standard finite element solutions with no discernible spectral leakage under periodic boundary conditions and near-perfect congruence after symmetric extension under non-periodic excitations.</p>