We propose a molecular-based three-dimensional (3D) continuum model of dragline silk of Araneus diadematus, which takes into account the plasticity of the β-sheet crystals, the rate-dependent behavior of the amorphous matrix, and the viscous interface friction between them. For the proposed model, we computed the tensile properties, the effects of velocity on the mechanical properties, and hysteresis values, which are in good agreement with available experimental data. The silk fiber model’s yield point, breaking strength, post-yield stiffness, and toughness increased with increasing pulling velocity, while extensibility and the diameter of the silk fiber decreased. Our bottom-up approach has shed light on silk fiber mechanics, which can be used as an essential tool to design artificial composite materials.