The modeling of humanoid robots with many degrees-of-freedom (DoF) can be done via the complete dynamic model. However, the complexity of the model can hide the essential factor of the walking, i.e. the equilibrium of the robot. One alternative is to simplify the model by neglecting some dynamical effects like in the 3D Linear Inverted Pendulum (LIP) model. Nonetheless, the assumption that the ZMP will be at the base of the pendulum is not ensured and the resulting walking gaits can make the Zero Moment Point (ZMP) evolves outside of the convex hull of support when they are replicated by the complete model of any humanoid robot. The objective of this paper is to propose a new model for walking that has the same dimensions as the 3D LIP model but considers the complete dynamics of the humanoid. The proposed model is called essential model and it can be written based on the internal states of the robot and/or external information, thereby generating models for different purposes. The main advantage of the essential model is that it allows to generate walking gaits that ensure that the Zero Moment Point (ZMP) is kept in a desired position or it follows a desired path while the gait is performed. Furthermore, impacts of the swing foot with the ground can be considered to compute periodic walking gaits. In order to show the advantages of the proposed model, numerical studies are performed to design periodic walking gaits for the humanoid robot ROMEO.