Abstract: The elasto-plastic constitutive model is widely applied in the performance analysis of engineering materials and structural components, characterized by significant path dependence and complicated nonlinear hysteresis. Accurately constructing an elasto-plastic constitutive model remains a challenging task. Currently, Recurrent Neural Networks (RNN) and their variants, taking deformation as input and force as output, can accurately represent the one-dimensional (1D) elasto-plastic constitutive relationship of components or materials. However, these methods involve tuning numerous hyperparameters and require solving a non-convex optimization problem, making the parameter tuning process time-consuming and unable to guarantee a global optimal solution. To address this issue, this paper proposes a new method called State Variable Guided Support Vector Machine (SVLS-SVM) to establish the uniaxial elasto-plastic constitutive model for construction materials or structural components. SVLS-SVM utilizes the state function of the modified tri-parameter hysteresis model to map the deformation input variables to the state space, forming state variables, thereby allowing the single-valued function between force and state variables to represent the complex multi-valued hysteresis relationship between force and deformation. Based on the experimental data of reinforced concrete columns with different failure modes and the elasto-plastic constitutive models of different construction materials, the accuracy and efficiency of the SVLS-SVM model are verified and compared with the RNN model. The results show that the SVLS-SVM model can accurately characterize the elasto-plastic hysteresis behavior of columns and materials, with a computational efficiency nearly 1177 times higher than that of the RNN.