Steel cylindrical shell structures such as silos and tanks are very sensitive to geometric imperfections and prone to a plastic instability failure known as elephant's foot (EF) buckling. This type of buckling arises under axial compression. The aim of this paper is to explore the plastic collapse response in conical shells with low semi-vertex angle values under compression. In a first step, the initial geometric imperfection shapes that dictate which plastic mechanisms arise were identified using finite element (FE) models. In a second step, a parametric study reported two plastic collapse mechanisms and showed that the elephant's foot plastic collapse mechanism is the most likely to appear in compressed conical shells with low d/t values, followed by the Yoshimura collapse mechanism, more common with larger d/t values. Finally, a practical model in which the parameters have been adjusted from numerical models has been derived for the elephant's foot plastic mechanism. This model provides the load-deformation behaviour of compressed conical shells at the post-collapse region. The load vs. end-shortening curves provided by the model have been validated through comparison with curves given by the FE models. The good agreement between the results proves the efficiency of the practical model to predict the collapse response of conical shells.