A detailed ride mathematical model of a full tracked vehicle, consisting of 17 dof, with trailing arm hydro-gas suspensions, is developed. The non-linear coupled governing differential equations of motion are derived for the sprung mass and fourteen unsprung masses, incorporating actual trailing arm kinematics and inertia coupling effects. The non-linear equations are solved using Matlab and validated using a multi-body dynamic model developed in MSC.Adams. Parametric studies and ride analyses have been carried out with different suspension characteristics, over random terrain. This full tracked vehicle mathematical vibration model is generic, computationally efficient and a useful tool for suspension design of tracked vehicles. © 2016 The Authors.