Abstract. The interaction between the solar wind and Earth's magnetosphere is a critical area of research in space weather and space physics. Accurate determination of the magnetopause position is essential for understanding magnetospheric dynamics. While numerous magnetopause models have been developed over past decades, most are time-independent, limiting their ability to elucidate the dynamic movement of the magnetopause under varying solar wind conditions. This study introduces the first time-dependent three-dimensional magnetopause model based on quasi-elastodynamic theory, named the POS (Position-Oscillation-Surface wave) model. Unlike existing time-independent models, the POS model physically reflects the dynamic responses of magnetopause position and shape to time-varying solar wind conditions. The predictive accuracy of the POS model was evaluated by using 38,887 observed magnetopause crossing events. The model achieved a root-mean-square error of 0.768 Earth radii (R_E), representing a 18.7 % improvement over five widely used magnetopause models. Notably, the POS model demonstrated superior accuracy under highly disturbed solar wind conditions (24.9 % better) and in higher latitude regions (28.7 % better) and flank regions (35.2 % better) of the magnetopause. The POS model's remarkable accuracy, concise formulation, and fast computational speed enhance our ability to predict magnetopause position and shape in real-time. This advancement is significant for understanding the physical mechanisms of space weather phenomena and improving the accuracy of space weather forecasts. Furthermore, this model may provide new insights and methodologies for constructing magnetopause models for other planets.