In this article, we present a new linear model (3LP) for bipedal locomotion which can describe swing and torso dynamics as well as falling. Compared to traditional inverted-pendulum based models, 3LP produces more human-like center of mass trajectory and swing motion which is missing in point-mass models. Different periodic gaits can be found with 3LP and modulated online without any numerical integration. Using linearity properties, we derive closed-form solutions and a transition matrix which describe state evolution over footsteps. This matrix as well as linear inequalities on inputs and states can be used in online model predictive controllers (MPC) to guaranty feasibility, robustness and optimality of the motion. Besides, 3LP can also be a powerful tool in bio-mechanics as it provides human-like ground reaction and torque profiles.