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This paper introduces a conceptual framework for finite element analysis of generalized Maxwell viscoelastic materials based on the initial stress approach. The proposed method facilitates the explicit and convenient determination of mechanical parameters for viscoelastic materials by directly utilizing relaxation test data. Each time step’s viscoelastic relaxation stress is treated as the initial stress, and a recursive calculation formula for the material’s initial stress is established, relying solely on the relaxation stress and strain from the previous time step. Based on this, the study outlines the computational steps for initial-stress-based finite element analysis of elastic materials. The proposed algorithm’s accuracy and efficiency are validated through a classical one-dimensional axial rod example. Results demonstrate that the introduced initial stress-type finite element analysis maintains the stiffness matrix equal to the initial stiffness matrix throughout the calculation process, significantly enhancing the efficiency of finite element analysis for viscoelastic materials while reducing the computational resource required. The conceptual framework improves the efficiency and accuracy of analyzing the mechanical parameters of viscoelastic materials using relaxation test data.