This work presents a novel mathematical model, formed by modifying the conventional Slab Model, to predict the behaviors of tube drawing with a floating plug in the hollow copper tubes. FEM and experimentation are employed to verify the analytical solution. The model incorporates some parameters, including as die semi-angle, plug semi-angle, friction coefficient and wall thickness reduction ratio. The Self Lock Effect is simulated using FEM, and the effect is useful in estimating the critical drawing force. The results of this work reveal that the new model is more accurate than the conventional Slab Model especially at reduction ratios of up to 40%.